Smallest and fastest sorting networks for a given number of inputs

Below are the best performing sorting networks known by the author for network sizes of up to 32 inputs, in terms of two metrics:

Provided is a minimum set of networks that each can be the best choice depending on how both criteria are weighted.

If no source is mentioned, the network was generated by the SorterHunter program, which in many cases matches pre-existing networks.

For a number of input sizes (n), the used method was able to reduce the upper bound for the minimal network size S(n) compared to the results reported by V. Valsalam & R. Miikkulainen [VM13]. This was the case for 18…23 inputs. For 24…26 and 28 inputs, a reduction was achieved vs. the Batcher odd-even merge of smaller networks, as listed in [Baddar09].

Also, for 25 and 26 inputs, a reduction in depth was achieved vs. the Batcher odd-even merge of smaller networks, lowering the optimal depth upper bound to 13 layers.

For questions, remarks, or to contribute improved results please contact bert.o.dobbelaere[at]telenet[dot]be.

Summary table

Number of inputs(Size,Depth) combinationsMin. size boundsMin. depth boundsComments
2(1, 1) 11Trivial
3(3, 3) 33[TAOCPv3]
4(5, 3) 53[TAOCPv3]
5(9, 5) 95[TAOCPv3]
6(12, 5) 125[TAOCPv3]
7(16, 6) 166[TAOCPv3]
8(19, 6) 196[TAOCPv3]
9(25, 7) 257[TAOCPv3], Optimal size proven in [CCFS16]
10(29, 8) (31, 7) 297[TAOCPv3], Optimal size proven in [CCFS16]
11(35, 8) 358[TAOCPv3], Optimal depth proven in [BZ14], optimal size proven by [Harder19]
12(39, 9) (40, 8) 398[TAOCPv3], Optimal depth proven in [BZ14], optimal size proven by [Harder19]
13(45, 10) (46, 9) 43…459[TAOCPv3], Optimal depth proven in [BZ14]
14(51, 10) (52, 9) 47…519[TAOCPv3], Optimal depth proven in [BZ14]
15(56, 10) (57, 9) 51…569[TAOCPv3], Optimal depth proven in [BZ14]
16(60, 10) (61, 9) 55…609[TAOCPv3], Optimal depth proven in [BZ14]
17(71, 12) (72, 11) (74, 10) 60…7110Size ubound: [Baddar09], depth ubound: [EM14], depth optimality: [CCEMS16]
18(77, 13) (78, 11) 65…7710…11Size ubound: SorterHunter, depth ubound: [Baddar09]
19(85, 12) (88, 11) 70…8510…11Size ubound: SorterHunter, depth ubound: [EM14].
20(91, 12) (93, 11) 75…9110…11Size ubound: SorterHunter, depth ubound: [EM14].
21(100, 12) 80…10010…12Size ubound: SorterHunter, depth ubound: [Baddar09]
22(107, 13) (108, 12) 85…10710…12Size ubound: SorterHunter, depth ubound: [Baddar09]
23(115, 13) (118, 12) 90…11510…12Size ubound: SorterHunter, depth ubound: [Ehlers17]
24(120, 13) (123, 12) 95…12010…12Size ubound: SorterHunter, depth ubound: [Ehlers17]
25(132, 15) (133, 14) (138, 13) 100…13210…13Depth ubound: SorterHunter. Size ubound: SorterHunter
26(139, 15) (140, 14) (145, 13) 105…13910…13Depth ubound: SorterHunter. Size ubound: SorterHunter
27(150, 15) (151, 14) 110…15010…14Size/depth ubounds: Batcher odd-even merge
28(155, 15) (157, 14) 115…15510…14Depth ubound: odd-even merge. Size ubound: SorterHunter
29(165, 15) (166, 14) 120…16510…14Size/depth ubounds: Batcher odd-even merge
30(172, 15) (173, 14) 125…17210…14Size/depth ubounds: Batcher odd-even merge
31(180, 14) 130…18010…14Size/depth ubounds: Batcher odd-even merge
32(185, 14) 135…18510…14Size/depth ubounds: Batcher odd-even merge

Individual networks:

Sorting network for 2 inputs, 1 CE, 1 layer:

[(0,1)]

Trivial sorting network for two inputs. The only simpler "network" is the one for one input, which uses no CE at all and is represented by a horizontal line.
Sorting network for 3 inputs, 3 CEs, 3 layers:

[(0,2)]
[(0,1)]
[(1,2)]

Sorting network for 4 inputs, 5 CEs, 3 layers:

[(0,2),(1,3)]
[(0,1),(2,3)]
[(1,2)]

Sorting network for 5 inputs, 9 CEs, 5 layers:

[(0,3),(1,4)]
[(0,2),(1,3)]
[(0,1),(2,4)]
[(1,2),(3,4)]
[(2,3)]

Sorting network for 6 inputs, 12 CEs, 5 layers:

[(0,5),(1,3),(2,4)]
[(1,2),(3,4)]
[(0,3),(2,5)]
[(0,1),(2,3),(4,5)]
[(1,2),(3,4)]

Sorting network for 7 inputs, 16 CEs, 6 layers:

[(0,6),(2,3),(4,5)]
[(0,2),(1,4),(3,6)]
[(0,1),(2,5),(3,4)]
[(1,2),(4,6)]
[(2,3),(4,5)]
[(1,2),(3,4),(5,6)]

Sorting network for 8 inputs, 19 CEs, 6 layers:

[(0,2),(1,3),(4,6),(5,7)]
[(0,4),(1,5),(2,6),(3,7)]
[(0,1),(2,3),(4,5),(6,7)]
[(2,4),(3,5)]
[(1,4),(3,6)]
[(1,2),(3,4),(5,6)]

Sorting network for 9 inputs, 25 CEs, 7 layers:

[(0,3),(1,7),(2,5),(4,8)]
[(0,7),(2,4),(3,8),(5,6)]
[(0,2),(1,3),(4,5),(7,8)]
[(1,4),(3,6),(5,7)]
[(0,1),(2,4),(3,5),(6,8)]
[(2,3),(4,5),(6,7)]
[(1,2),(3,4),(5,6)]

Sorting network for 10 inputs, 29 CEs, 8 layers:

[(0,8),(1,9),(2,7),(3,5),(4,6)]
[(0,2),(1,4),(5,8),(7,9)]
[(0,3),(2,4),(5,7),(6,9)]
[(0,1),(3,6),(8,9)]
[(1,5),(2,3),(4,8),(6,7)]
[(1,2),(3,5),(4,6),(7,8)]
[(2,3),(4,5),(6,7)]
[(3,4),(5,6)]

Sorting network for 10 inputs, 31 CEs, 7 layers:

[(0,1),(2,5),(3,6),(4,7),(8,9)]
[(0,6),(1,8),(2,4),(3,9),(5,7)]
[(0,2),(1,3),(4,5),(6,8),(7,9)]
[(0,1),(2,7),(3,5),(4,6),(8,9)]
[(1,2),(3,4),(5,6),(7,8)]
[(1,3),(2,4),(5,7),(6,8)]
[(2,3),(4,5),(6,7)]

31 is the optimal size for 7 layers [Fon18]
Sorting network for 11 inputs, 35 CEs, 8 layers:

[(0,9),(1,6),(2,4),(3,7),(5,8)]
[(0,1),(3,5),(4,10),(6,9),(7,8)]
[(1,3),(2,5),(4,7),(8,10)]
[(0,4),(1,2),(3,7),(5,9),(6,8)]
[(0,1),(2,6),(4,5),(7,8),(9,10)]
[(2,4),(3,6),(5,7),(8,9)]
[(1,2),(3,4),(5,6),(7,8)]
[(2,3),(4,5),(6,7)]

35 is the optimal size [Harder19] (see also [Fon18] for 8 or 9 layers).
Sorting network for 12 inputs, 39 CEs, 9 layers:

[(0,8),(1,7),(2,6),(3,11),(4,10),(5,9)]
[(0,1),(2,5),(3,4),(6,9),(7,8),(10,11)]
[(0,2),(1,6),(5,10),(9,11)]
[(0,3),(1,2),(4,6),(5,7),(8,11),(9,10)]
[(1,4),(3,5),(6,8),(7,10)]
[(1,3),(2,5),(6,9),(8,10)]
[(2,3),(4,5),(6,7),(8,9)]
[(4,6),(5,7)]
[(3,4),(5,6),(7,8)]

39 is the optimal size [Harder19] (see also [Fon18] for 9 layers).
Sorting network for 12 inputs, 40 CEs, 8 layers:

[(0,8),(1,7),(2,6),(3,11),(4,10),(5,9)]
[(0,2),(1,4),(3,5),(6,8),(7,10),(9,11)]
[(0,1),(2,9),(4,7),(5,6),(10,11)]
[(1,3),(2,7),(4,9),(8,10)]
[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11)]
[(1,2),(3,5),(6,8),(9,10)]
[(2,4),(3,6),(5,8),(7,9)]
[(1,2),(3,4),(5,6),(7,8),(9,10)]

40 is the optimal size for 8 layers [Fon18].
Sorting network for 13 inputs, 45 CEs, 10 layers:

[(0,12),(1,10),(2,9),(3,7),(5,11),(6,8)]
[(1,6),(2,3),(4,11),(7,9),(8,10)]
[(0,4),(1,2),(3,6),(7,8),(9,10),(11,12)]
[(4,6),(5,9),(8,11),(10,12)]
[(0,5),(3,8),(4,7),(6,11),(9,10)]
[(0,1),(2,5),(6,9),(7,8),(10,11)]
[(1,3),(2,4),(5,6),(9,10)]
[(1,2),(3,4),(5,7),(6,8)]
[(2,3),(4,5),(6,7),(8,9)]
[(3,4),(5,6)]

Sorting network for 13 inputs, 46 CEs, 9 layers:

[(0,11),(1,7),(2,4),(3,5),(8,9),(10,12)]
[(0,2),(3,6),(4,12),(5,7),(8,10)]
[(0,8),(1,3),(2,5),(4,9),(6,11),(7,12)]
[(0,1),(2,10),(3,8),(4,6),(9,11)]
[(1,3),(2,4),(5,10),(6,8),(7,9),(11,12)]
[(1,2),(3,4),(5,8),(6,9),(7,10)]
[(2,3),(4,7),(5,6),(8,11),(9,10)]
[(4,5),(6,7),(8,9),(10,11)]
[(3,4),(5,6),(7,8),(9,10)]

Sorting network for 14 inputs, 51 CEs, 10 layers:

[(0,6),(1,11),(2,12),(3,10),(4,5),(7,13),(8,9)]
[(1,2),(3,7),(4,8),(5,9),(6,10),(11,12)]
[(0,4),(1,3),(5,6),(7,8),(9,13),(10,12)]
[(0,1),(2,9),(3,7),(4,11),(6,10),(12,13)]
[(2,5),(4,7),(6,9),(8,11)]
[(1,2),(3,4),(6,7),(9,10),(11,12)]
[(1,3),(2,4),(5,6),(7,8),(9,11),(10,12)]
[(2,3),(4,7),(6,9),(10,11)]
[(4,5),(6,7),(8,9)]
[(3,4),(5,6),(7,8),(9,10)]

Sorting network for 14 inputs, 52 CEs, 9 layers:

[(0,3),(1,9),(2,6),(4,12),(5,10),(7,11),(8,13)]
[(0,2),(3,12),(4,5),(6,10),(7,8),(11,13)]
[(0,1),(2,11),(3,6),(4,7),(5,9),(10,12)]
[(0,4),(1,7),(2,5),(3,8),(6,13),(9,11)]
[(1,2),(3,4),(5,7),(6,9),(8,10),(12,13)]
[(1,3),(2,4),(5,9),(6,10),(7,8),(11,12)]
[(2,3),(4,5),(6,7),(8,11),(9,10),(12,13)]
[(4,6),(5,7),(8,9),(10,11)]
[(3,4),(5,6),(7,8),(9,10),(11,12)]

Sorting network for 15 inputs, 56 CEs, 10 layers:

[(1,2),(3,10),(4,14),(5,8),(6,13),(7,12),(9,11)]
[(0,14),(1,5),(2,8),(3,7),(6,9),(10,12),(11,13)]
[(0,7),(1,6),(2,9),(4,10),(5,11),(8,13),(12,14)]
[(0,6),(2,4),(3,5),(7,11),(8,10),(9,12),(13,14)]
[(0,3),(1,2),(4,7),(5,9),(6,8),(10,11),(12,13)]
[(0,1),(2,3),(4,6),(7,9),(10,12),(11,13)]
[(1,2),(3,5),(8,10),(11,12)]
[(3,4),(5,6),(7,8),(9,10)]
[(2,3),(4,5),(6,7),(8,9),(10,11)]
[(5,6),(7,8)]

Sorting network for 15 inputs, 57 CEs, 9 layers:

[(0,6),(1,10),(2,14),(3,9),(4,12),(5,13),(7,11)]
[(0,7),(2,5),(3,4),(6,11),(8,10),(9,12),(13,14)]
[(1,13),(2,3),(4,6),(5,9),(7,8),(10,14),(11,12)]
[(0,3),(1,4),(5,7),(6,13),(8,9),(10,11),(12,14)]
[(0,2),(1,5),(3,8),(4,6),(7,10),(9,11),(12,13)]
[(0,1),(2,5),(3,10),(4,8),(6,7),(9,12),(11,13)]
[(1,2),(3,4),(5,6),(7,9),(8,10),(11,12)]
[(3,5),(4,6),(7,8),(9,10)]
[(2,3),(4,5),(6,7),(8,9),(10,11)]

Sorting network for 16 inputs, 60 CEs, 10 layers:

[(0,13),(1,12),(2,15),(3,14),(4,8),(5,6),(7,11),(9,10)]
[(0,5),(1,7),(2,9),(3,4),(6,13),(8,14),(10,15),(11,12)]
[(0,1),(2,3),(4,5),(6,8),(7,9),(10,11),(12,13),(14,15)]
[(0,2),(1,3),(4,10),(5,11),(6,7),(8,9),(12,14),(13,15)]
[(1,2),(3,12),(4,6),(5,7),(8,10),(9,11),(13,14)]
[(1,4),(2,6),(5,8),(7,10),(9,13),(11,14)]
[(2,4),(3,6),(9,12),(11,13)]
[(3,5),(6,8),(7,9),(10,12)]
[(3,4),(5,6),(7,8),(9,10),(11,12)]
[(6,7),(8,9)]

Size and depth match the handcrafted network of M.W. Green, 1969 [TAOCPv3]. It is remarkable that the last three layers (found by independent computer search) are identical to those in Green's network.
Sorting network for 16 inputs, 61 CEs, 9 layers:

[(0,5),(1,4),(2,12),(3,13),(6,7),(8,9),(10,15),(11,14)]
[(0,2),(1,10),(3,6),(4,7),(5,14),(8,11),(9,12),(13,15)]
[(0,8),(1,3),(2,11),(4,13),(5,9),(6,10),(7,15),(12,14)]
[(0,1),(2,4),(3,8),(5,6),(7,12),(9,10),(11,13),(14,15)]
[(1,3),(2,5),(4,8),(6,9),(7,11),(10,13),(12,14)]
[(1,2),(3,5),(4,11),(6,8),(7,9),(10,12),(13,14)]
[(2,3),(4,5),(6,7),(8,9),(10,11),(12,13)]
[(4,6),(5,7),(8,10),(9,11)]
[(3,4),(5,6),(7,8),(9,10),(11,12)]

Sorting network for 17 inputs, 71 CEs, 12 layers:

[(0,11),(1,15),(2,10),(3,5),(4,6),(8,12),(9,16),(13,14)]
[(0,6),(1,13),(2,8),(4,14),(5,15),(7,11)]
[(0,8),(3,7),(4,9),(6,16),(10,11),(12,14)]
[(0,2),(1,4),(5,6),(7,13),(8,9),(10,12),(11,14),(15,16)]
[(0,3),(2,5),(6,11),(7,10),(9,13),(12,15),(14,16)]
[(0,1),(3,4),(5,10),(6,9),(7,8),(11,15),(13,14)]
[(1,2),(3,7),(4,8),(6,12),(11,13),(14,15)]
[(1,3),(2,7),(4,5),(9,11),(10,12),(13,14)]
[(2,3),(4,6),(5,7),(8,10)]
[(3,4),(6,8),(7,9),(10,12)]
[(5,6),(7,8),(9,10),(11,12)]
[(4,5),(6,7),(8,9),(10,11),(12,13)]

Size matches result from Valsalam & Miikkulainen [VM13]. Depth reduced from 17 to 12.
Sorting network for 17 inputs, 72 CEs, 11 layers:

[(0,8),(1,3),(2,6),(4,15),(5,13),(9,16),(10,11),(12,14)]
[(0,2),(1,4),(3,15),(5,8),(6,14),(7,9),(13,16)]
[(2,13),(3,11),(5,10),(6,9),(7,12),(8,15),(14,16)]
[(0,7),(1,5),(3,6),(4,10),(8,14),(9,11),(12,13),(15,16)]
[(0,1),(2,6),(4,12),(5,7),(9,14),(10,13),(11,15)]
[(1,4),(2,3),(6,11),(7,12),(8,9),(13,14),(15,16)]
[(2,5),(3,8),(7,10),(9,12),(11,13),(14,15)]
[(1,2),(3,7),(4,5),(6,9),(8,10),(13,14)]
[(3,4),(5,7),(6,8),(9,11),(10,12)]
[(2,4),(5,6),(7,8),(9,10),(11,12)]
[(2,3),(4,5),(6,7),(8,9),(10,11),(12,13)]

Sorting network for 17 inputs, 74 CEs, 10 layers:

[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16)]
[(1,3),(2,4),(5,7),(6,8),(9,11),(10,12),(13,15),(14,16)]
[(1,5),(2,6),(3,7),(4,8),(9,13),(10,14),(11,15),(12,16)]
[(0,3),(1,13),(2,10),(4,7),(5,11),(6,12),(8,9),(14,15)]
[(0,13),(1,8),(2,5),(3,6),(4,14),(7,15),(9,16),(10,11)]
[(0,1),(2,8),(3,4),(5,10),(6,13),(7,11),(12,14)]
[(1,5),(3,8),(4,10),(6,7),(9,12),(11,13)]
[(1,2),(4,6),(5,8),(7,10),(9,11),(12,14),(13,15)]
[(2,3),(4,5),(6,8),(7,9),(10,11),(12,13),(14,15)]
[(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16)]

This network was obtained by performing a size optimization of the network found by Ehlers&Müller (see [EM14])
Sorting network for 18 inputs, 77 CEs, 13 layers:

[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17)]
[(1,5),(2,6),(3,7),(4,10),(8,16),(9,17),(12,14),(13,15)]
[(0,8),(1,10),(2,12),(3,14),(6,13),(7,15),(9,16),(11,17)]
[(0,4),(1,9),(5,17),(8,11),(10,16)]
[(0,2),(1,6),(4,10),(5,9),(14,16),(15,17)]
[(1,2),(3,10),(4,12),(5,7),(6,14),(9,13),(15,16)]
[(3,8),(5,12),(7,11),(9,10)]
[(3,4),(6,8),(7,14),(9,12),(11,13)]
[(1,3),(2,4),(7,9),(8,12),(11,15),(13,16)]
[(2,3),(4,5),(6,7),(10,11),(12,14),(13,15)]
[(4,6),(5,8),(9,10),(11,14)]
[(3,4),(5,7),(8,9),(10,12),(13,14)]
[(5,6),(7,8),(9,10),(11,12)]

Asymmetric network with improved size over result (78) reported in [VM13].
Sorting network for 18 inputs, 78 CEs, 11 layers:

[(0,6),(1,10),(2,15),(3,5),(4,9),(7,16),(8,13),(11,17),(12,14)]
[(0,12),(1,4),(3,11),(5,17),(6,14),(7,8),(9,10),(13,16)]
[(1,13),(2,7),(4,16),(6,9),(8,11),(10,15)]
[(0,1),(2,3),(4,12),(5,13),(7,9),(8,10),(14,15),(16,17)]
[(0,2),(1,11),(3,4),(5,7),(6,16),(10,12),(13,14),(15,17)]
[(1,8),(4,10),(5,6),(7,13),(9,16),(11,12)]
[(1,3),(2,5),(4,7),(6,8),(9,11),(10,13),(12,15),(14,16)]
[(1,2),(3,5),(4,6),(7,9),(8,10),(11,13),(12,14),(15,16)]
[(2,3),(5,8),(6,7),(9,12),(10,11),(14,15)]
[(3,4),(5,6),(7,8),(9,10),(11,12),(13,14)]
[(4,5),(6,7),(8,9),(10,11),(12,13)]

Matches depth of 11 layers reported in [Baddar09] while reducing size from 84 to 78.
Sorting network for 19 inputs, 85 CEs, 12 layers:

[(0,12),(1,4),(2,8),(3,5),(6,17),(7,11),(9,14),(10,13),(15,16)]
[(0,2),(1,7),(3,6),(4,11),(5,17),(8,12),(10,15),(13,16),(14,18)]
[(3,10),(4,14),(5,15),(6,13),(7,9),(11,17),(16,18)]
[(0,7),(1,10),(4,6),(9,15),(11,16),(12,17),(13,14)]
[(0,3),(2,6),(5,7),(8,11),(12,16)]
[(1,8),(2,9),(3,4),(6,15),(7,13),(10,11),(12,18)]
[(1,3),(2,5),(6,9),(7,12),(8,10),(11,14),(17,18)]
[(0,1),(2,3),(4,8),(6,10),(9,12),(14,15),(16,17)]
[(1,2),(5,8),(6,7),(9,11),(10,13),(14,16),(15,17)]
[(3,6),(4,5),(7,9),(8,10),(11,12),(13,14),(15,16)]
[(3,4),(5,6),(7,8),(9,10),(11,13),(12,14)]
[(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15)]

Improved size over result (86) reported by Valsalam & Miikkulainen [VM13]
Sorting network for 19 inputs, 88 CEs, 11 layers:

[(0,12),(1,13),(2,14),(3,15),(4,16),(5,17),(6,18),(8,10),(9,11)]
[(0,2),(1,3),(4,6),(5,7),(8,9),(10,11),(12,14),(13,15),(16,18)]
[(0,1),(2,3),(4,5),(6,7),(12,13),(14,15),(16,17)]
[(0,4),(1,12),(2,16),(3,17),(5,8),(6,9),(7,18),(10,13),(11,14)]
[(1,6),(3,10),(4,5),(7,11),(8,12),(9,16),(13,18),(14,15)]
[(0,4),(2,8),(3,9),(6,7),(10,16),(11,17),(12,13),(15,18)]
[(1,4),(3,6),(5,8),(7,10),(9,12),(11,14),(13,16)]
[(2,3),(4,5),(6,8),(7,9),(10,12),(11,13),(14,15),(16,17)]
[(2,4),(3,6),(5,7),(8,10),(9,11),(12,14),(13,16),(15,17)]
[(1,2),(3,5),(6,7),(8,9),(10,11),(12,13),(14,16),(17,18)]
[(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16)]

Obtained by removing highest input from 20 inputs case with depth 11.
Sorting network for 20 inputs, 91 CEs, 12 layers:

[(0,3),(1,7),(2,5),(4,8),(6,9),(10,13),(11,15),(12,18),(14,17),(16,19)]
[(0,14),(1,11),(2,16),(3,17),(4,12),(5,19),(6,10),(7,15),(8,18),(9,13)]
[(0,4),(1,2),(3,8),(5,7),(11,16),(12,14),(15,19),(17,18)]
[(1,6),(2,12),(3,5),(4,11),(7,17),(8,15),(13,18),(14,16)]
[(0,1),(2,6),(7,10),(9,12),(13,17),(18,19)]
[(1,6),(5,9),(7,11),(8,12),(10,14),(13,18)]
[(3,5),(4,7),(8,10),(9,11),(12,15),(14,16)]
[(1,3),(2,4),(5,7),(6,10),(9,13),(12,14),(15,17),(16,18)]
[(1,2),(3,4),(6,7),(8,9),(10,11),(12,13),(15,16),(17,18)]
[(2,3),(4,6),(5,8),(7,9),(10,12),(11,14),(13,15),(16,17)]
[(4,5),(6,8),(7,10),(9,12),(11,13),(14,15)]
[(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16)]

Improved size over result (92) reported by Valsalam & Miikkulainen [VM13]
Sorting network for 20 inputs, 93 CEs, 11 layers:

[(0,12),(1,13),(2,14),(3,15),(4,16),(5,17),(6,18),(7,19),(8,10),(9,11)]
[(0,2),(1,3),(4,6),(5,7),(8,9),(10,11),(12,14),(13,15),(16,18),(17,19)]
[(0,1),(2,3),(4,5),(6,7),(12,13),(14,15),(16,17),(18,19)]
[(0,4),(1,12),(2,16),(3,17),(5,8),(6,9),(7,18),(10,13),(11,14),(15,19)]
[(1,6),(3,10),(4,5),(7,11),(8,12),(9,16),(13,18),(14,15)]
[(0,4),(2,8),(3,9),(6,7),(10,16),(11,17),(12,13),(15,19)]
[(1,4),(3,6),(5,8),(7,10),(9,12),(11,14),(13,16),(15,18)]
[(2,3),(4,5),(6,8),(7,9),(10,12),(11,13),(14,15),(16,17)]
[(2,4),(3,6),(5,7),(8,10),(9,11),(12,14),(13,16),(15,17)]
[(1,2),(3,5),(6,7),(8,9),(10,11),(12,13),(14,16),(17,18)]
[(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16)]

First 3 layers inspired by [EM14]
Sorting network for 21 inputs, 100 CEs, 12 layers:

[(0,7),(1,10),(3,5),(4,8),(6,13),(9,19),(11,14),(12,17),(15,16),(18,20)]
[(0,11),(1,15),(2,12),(3,4),(5,8),(6,9),(7,14),(10,16),(13,19),(17,20)]
[(0,6),(1,3),(2,18),(4,15),(5,10),(8,16),(11,17),(12,13),(14,20)]
[(2,6),(5,12),(7,18),(8,14),(9,11),(10,17),(13,19),(16,20)]
[(1,2),(4,7),(5,9),(6,17),(10,13),(11,12),(14,19),(15,18)]
[(0,2),(3,6),(4,5),(7,10),(8,11),(9,15),(12,16),(13,18),(14,17),(19,20)]
[(0,1),(2,3),(5,9),(6,12),(7,8),(11,14),(13,15),(16,19),(17,18)]
[(1,2),(3,9),(6,13),(10,11),(12,15),(16,17),(18,19)]
[(1,4),(2,5),(3,7),(6,10),(8,9),(11,12),(13,14),(17,18)]
[(2,4),(5,6),(7,8),(9,11),(10,13),(12,15),(14,16)]
[(3,4),(5,7),(6,8),(9,10),(11,13),(12,14),(15,16)]
[(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17)]

Improved size over result (102) reported by Valsalam & Miikkulainen [VM13], combined with lowest known depth.
Sorting network for 22 inputs, 107 CEs, 13 layers:

[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21)]
[(0,12),(1,13),(2,6),(3,7),(4,10),(8,20),(9,21),(11,17),(14,18),(15,19)]
[(0,2),(1,6),(3,12),(4,16),(5,17),(7,13),(8,14),(9,18),(15,20),(19,21)]
[(0,8),(1,15),(2,14),(3,9),(5,11),(6,20),(7,19),(10,16),(12,18),(13,21)]
[(0,4),(1,10),(3,8),(5,9),(7,14),(11,20),(12,16),(13,18),(17,21)]
[(1,3),(2,5),(4,8),(6,9),(7,10),(11,14),(12,15),(13,17),(16,19),(18,20)]
[(2,4),(3,12),(5,8),(6,11),(9,18),(10,15),(13,16),(17,19)]
[(1,2),(3,4),(5,7),(6,12),(8,11),(9,15),(10,13),(14,16),(17,18),(19,20)]
[(2,3),(4,5),(7,12),(8,10),(9,14),(11,13),(16,17),(18,19)]
[(4,6),(5,8),(9,11),(10,12),(13,16),(15,17)]
[(3,4),(6,7),(9,10),(11,12),(14,15),(17,18)]
[(5,6),(7,8),(10,11),(13,14),(15,16)]
[(6,7),(8,9),(12,13),(14,15)]

Improved size over result (108) reported by Valsalam & Miikkulainen [VM13]
Sorting network for 22 inputs, 108 CEs, 12 layers:

[(0,14),(1,8),(2,4),(3,5),(6,11),(7,21),(9,12),(10,15),(13,20),(16,18),(17,19)]
[(0,7),(1,13),(2,17),(3,16),(4,19),(5,18),(6,10),(8,20),(11,15),(14,21)]
[(0,1),(3,6),(4,9),(5,10),(7,13),(8,14),(11,16),(12,17),(15,18),(20,21)]
[(0,3),(1,8),(2,4),(7,11),(9,12),(10,14),(13,20),(17,19),(18,21)]
[(1,6),(2,7),(3,17),(4,18),(5,11),(8,9),(10,16),(12,13),(14,19),(15,20)]
[(0,2),(3,7),(4,6),(5,8),(9,11),(10,12),(13,16),(14,18),(15,17),(19,21)]
[(1,4),(3,5),(6,13),(7,9),(8,15),(12,14),(16,18),(17,20)]
[(1,2),(4,10),(6,12),(7,8),(9,15),(11,17),(13,14),(19,20)]
[(1,3),(2,5),(6,10),(8,9),(11,15),(12,13),(16,19),(18,20)]
[(2,3),(4,8),(5,7),(6,9),(10,11),(12,15),(13,17),(14,16),(18,19)]
[(4,5),(6,7),(8,10),(9,12),(11,13),(14,15),(16,17)]
[(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18)]

Size matches result from Valsalam & Miikkulainen [VM13]. Depth reduced from 15 to 12.
Sorting network for 23 inputs, 115 CEs, 13 layers:

[(0,20),(1,12),(2,16),(4,6),(5,10),(7,21),(8,14),(9,15),(11,22),(13,18),(17,19)]
[(0,3),(1,11),(2,7),(4,17),(5,13),(6,19),(8,9),(10,18),(12,22),(14,15),(16,21)]
[(0,1),(2,4),(3,12),(5,8),(6,9),(7,10),(11,20),(13,16),(14,17),(15,18),(19,21)]
[(2,5),(4,8),(6,11),(7,14),(9,16),(12,17),(15,19),(18,21)]
[(1,8),(3,14),(4,7),(9,20),(10,12),(11,13),(15,22),(16,19)]
[(0,7),(1,5),(3,4),(6,11),(8,15),(9,14),(10,13),(12,17),(18,22),(19,20)]
[(0,2),(1,6),(4,7),(5,9),(8,10),(13,15),(14,18),(16,19),(17,22),(20,21)]
[(2,3),(4,5),(6,8),(7,9),(10,11),(12,13),(14,16),(15,17),(18,19),(21,22)]
[(1,2),(3,6),(4,10),(7,8),(9,11),(12,14),(13,19),(15,16),(17,20)]
[(2,3),(5,10),(6,7),(8,9),(13,18),(14,15),(16,17),(20,21)]
[(3,4),(5,7),(10,12),(11,13),(16,18),(19,20)]
[(4,6),(8,10),(9,12),(11,14),(13,15),(17,19)]
[(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18)]

Obtained by removing highest input from 24 inputs case with 13 layers. Reduction in size vs. 118 reported in [Baddar09]
Sorting network for 23 inputs, 118 CEs, 12 layers:

[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21)]
[(0,2),(1,3),(4,6),(5,7),(8,10),(9,11),(12,14),(13,15),(16,18),(17,19),(20,22)]
[(0,4),(1,5),(2,8),(3,9),(6,10),(7,11),(12,16),(13,17),(14,20),(15,21),(18,22)]
[(0,2),(1,3),(4,6),(5,7),(8,10),(9,11),(12,14),(13,15),(16,18),(17,19),(20,22)]
[(0,12),(1,13),(2,4),(3,5),(6,8),(7,9),(10,22),(14,16),(15,17),(18,20),(19,21)]
[(1,12),(2,14),(3,15),(4,16),(5,17),(6,18),(7,19),(8,20),(9,21),(11,22)]
[(1,2),(3,14),(4,6),(5,7),(8,13),(9,20),(10,15),(16,18),(17,19),(21,22)]
[(3,6),(5,16),(7,18),(8,12),(9,13),(10,14),(11,15),(17,20)]
[(2,3),(4,8),(5,12),(6,10),(7,14),(9,16),(11,18),(13,17),(15,19),(20,21)]
[(2,4),(5,8),(7,9),(10,12),(11,13),(14,16),(15,18),(19,21)]
[(3,5),(6,8),(7,10),(9,12),(11,14),(13,16),(15,17),(18,20)]
[(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20)]

Obtained by removing highest input from 24 inputs case with 12 layers
Sorting network for 24 inputs, 120 CEs, 13 layers:

[(0,20),(1,12),(2,16),(3,23),(4,6),(5,10),(7,21),(8,14),(9,15),(11,22),(13,18),(17,19)]
[(0,3),(1,11),(2,7),(4,17),(5,13),(6,19),(8,9),(10,18),(12,22),(14,15),(16,21),(20,23)]
[(0,1),(2,4),(3,12),(5,8),(6,9),(7,10),(11,20),(13,16),(14,17),(15,18),(19,21),(22,23)]
[(2,5),(4,8),(6,11),(7,14),(9,16),(12,17),(15,19),(18,21)]
[(1,8),(3,14),(4,7),(9,20),(10,12),(11,13),(15,22),(16,19)]
[(0,7),(1,5),(3,4),(6,11),(8,15),(9,14),(10,13),(12,17),(16,23),(18,22),(19,20)]
[(0,2),(1,6),(4,7),(5,9),(8,10),(13,15),(14,18),(16,19),(17,22),(21,23)]
[(2,3),(4,5),(6,8),(7,9),(10,11),(12,13),(14,16),(15,17),(18,19),(20,21)]
[(1,2),(3,6),(4,10),(7,8),(9,11),(12,14),(13,19),(15,16),(17,20),(21,22)]
[(2,3),(5,10),(6,7),(8,9),(13,18),(14,15),(16,17),(20,21)]
[(3,4),(5,7),(10,12),(11,13),(16,18),(19,20)]
[(4,6),(8,10),(9,12),(11,14),(13,15),(17,19)]
[(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18)]

Reduction in size vs. 123 reported in [Baddar09]
Sorting network for 24 inputs, 123 CEs, 12 layers:

[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21),(22,23)]
[(0,2),(1,3),(4,6),(5,7),(8,10),(9,11),(12,14),(13,15),(16,18),(17,19),(20,22),(21,23)]
[(0,4),(1,5),(2,8),(3,9),(6,10),(7,11),(12,16),(13,17),(14,20),(15,21),(18,22),(19,23)]
[(0,2),(1,3),(4,6),(5,7),(8,10),(9,11),(12,14),(13,15),(16,18),(17,19),(20,22),(21,23)]
[(0,12),(1,13),(2,4),(3,5),(6,8),(7,9),(10,22),(11,23),(14,16),(15,17),(18,20),(19,21)]
[(1,12),(2,14),(3,15),(4,16),(5,17),(6,18),(7,19),(8,20),(9,21),(11,22)]
[(1,2),(3,14),(4,6),(5,7),(8,13),(9,20),(10,15),(16,18),(17,19),(21,22)]
[(3,6),(5,16),(7,18),(8,12),(9,13),(10,14),(11,15),(17,20)]
[(2,3),(4,8),(5,12),(6,10),(7,14),(9,16),(11,18),(13,17),(15,19),(20,21)]
[(2,4),(5,8),(7,9),(10,12),(11,13),(14,16),(15,18),(19,21)]
[(3,5),(6,8),(7,10),(9,12),(11,14),(13,16),(15,17),(18,20)]
[(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20)]

Prefix layers obtained from [Ehlers17]. Further optimized for size.
Sorting network for 25 inputs, 132 CEs, 15 layers:

[(0,2),(1,8),(3,18),(4,17),(5,20),(6,19),(7,9),(10,11),(12,13),(14,16),(15,22),(21,23)]
[(0,3),(1,15),(2,18),(4,12),(5,21),(6,10),(7,14),(8,22),(9,16),(11,19),(13,17),(20,23)]
[(0,4),(1,7),(2,13),(3,12),(5,6),(8,14),(9,15),(10,21),(11,20),(16,22),(17,18),(19,23)]
[(0,5),(2,11),(3,6),(4,10),(7,16),(8,9),(12,21),(13,19),(14,15),(17,20),(18,23)]
[(2,7),(6,9),(8,11),(14,24),(18,21)]
[(3,8),(7,10),(11,12),(13,14),(15,21),(18,20),(22,24)]
[(4,13),(10,16),(11,15),(18,24),(19,22)]
[(1,4),(8,11),(9,19),(13,17),(14,18),(16,20),(23,24)]
[(0,1),(4,5),(6,13),(9,14),(10,17),(12,16),(18,19),(20,21),(22,23)]
[(2,6),(3,4),(5,13),(7,9),(12,18),(15,17),(16,19),(20,22),(21,23)]
[(1,2),(5,8),(6,7),(9,10),(11,13),(14,15),(17,20),(21,22)]
[(1,3),(2,4),(5,6),(7,11),(8,9),(10,13),(12,14),(15,16),(17,18),(19,20)]
[(2,3),(4,8),(6,7),(9,12),(10,11),(13,14),(15,17),(16,18),(20,21)]
[(3,5),(4,6),(7,8),(9,10),(11,12),(13,15),(14,17),(16,19)]
[(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19)]

Improved size over 133 that could be obtained by Batcher odd-even merge with same depth
Sorting network for 25 inputs, 133 CEs, 14 layers:

[(0,2),(1,8),(3,18),(4,17),(5,20),(6,19),(7,9),(10,11),(12,13),(14,16),(15,22),(21,23)]
[(0,3),(1,15),(2,18),(4,12),(5,21),(6,10),(7,14),(8,22),(9,16),(11,19),(13,17),(20,23)]
[(0,4),(1,7),(2,13),(3,12),(5,6),(8,14),(9,15),(10,21),(11,20),(16,22),(17,18),(19,23)]
[(0,5),(2,11),(3,6),(4,10),(8,9),(12,21),(13,19),(14,15),(17,20),(18,23),(22,24)]
[(7,12),(8,10),(9,13),(11,22),(18,21),(19,20),(23,24)]
[(1,11),(3,8),(4,9),(5,7),(6,13),(10,15),(14,18),(16,22)]
[(2,5),(7,17),(11,14),(15,21),(16,19),(18,23),(20,22)]
[(1,5),(6,14),(9,11),(10,17),(12,16),(15,20),(18,19),(22,23)]
[(0,1),(4,9),(5,6),(7,12),(8,10),(13,14),(15,18),(16,17),(19,22),(20,21)]
[(1,2),(3,4),(5,8),(6,10),(7,9),(11,12),(13,16),(14,17),(19,20),(21,22)]
[(1,3),(2,4),(5,7),(6,9),(8,11),(10,12),(13,15),(14,18),(16,19),(17,20),(22,23)]
[(2,3),(4,7),(6,8),(9,11),(10,13),(12,14),(15,16),(17,19),(20,21)]
[(3,5),(4,6),(7,8),(9,10),(11,13),(12,15),(14,16),(17,18)]
[(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19)]

Improved size over 134 that could be obtained by Batcher odd-even merge with same depth
Sorting network for 25 inputs, 138 CEs, 13 layers:

[(0,13),(1,6),(2,8),(3,20),(4,7),(5,22),(9,16),(10,15),(11,14),(17,23),(18,21),(19,24)]
[(0,3),(1,19),(4,18),(5,12),(6,24),(7,21),(8,16),(9,17),(10,11),(13,20),(14,15)]
[(0,10),(1,5),(2,17),(3,12),(6,11),(7,16),(8,23),(9,18),(13,22),(14,19),(20,24)]
[(0,1),(2,9),(3,14),(4,8),(5,10),(6,13),(7,18),(11,22),(12,19),(15,20),(16,23),(17,21)]
[(1,5),(2,4),(3,6),(7,9),(8,17),(10,15),(11,14),(12,13),(16,18),(19,22),(20,24),(21,23)]
[(0,2),(1,3),(4,7),(5,6),(8,10),(9,16),(11,12),(13,14),(15,17),(18,21),(19,20),(22,24)]
[(1,2),(3,4),(6,18),(7,19),(8,11),(9,12),(10,15),(13,16),(14,17),(21,22),(23,24)]
[(1,9),(2,11),(4,6),(5,7),(10,12),(13,15),(14,23),(18,20),(19,21)]
[(1,3),(2,8),(6,14),(7,13),(9,10),(11,19),(12,18),(15,16),(17,23),(20,22)]
[(2,5),(4,9),(6,10),(7,8),(11,13),(12,14),(15,19),(16,21),(17,18),(20,23)]
[(3,5),(4,7),(6,11),(8,9),(10,12),(13,15),(14,19),(16,17),(18,21),(22,23)]
[(2,3),(5,7),(6,8),(9,11),(10,13),(12,15),(14,16),(17,19),(18,20)]
[(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21)]

Improved depth over 14 that could be obtained by Batcher odd-even merge
Sorting network for 26 inputs, 139 CEs, 15 layers:

[(0,25),(1,3),(2,9),(4,19),(5,18),(6,21),(7,20),(8,10),(11,12),(13,14),(15,17),(16,23),(22,24)]
[(1,4),(2,16),(3,19),(5,13),(6,22),(7,11),(8,15),(9,23),(10,17),(12,20),(14,18),(21,24)]
[(1,5),(2,8),(3,14),(4,13),(6,7),(9,15),(10,16),(11,22),(12,21),(17,23),(18,19),(20,24)]
[(0,10),(1,6),(3,7),(4,11),(5,12),(13,20),(14,21),(15,25),(18,22),(19,24)]
[(0,4),(8,10),(12,13),(15,17),(21,25)]
[(0,2),(4,8),(10,12),(13,15),(17,21),(23,25)]
[(0,1),(2,3),(4,5),(8,14),(9,13),(11,17),(12,16),(20,21),(22,23),(24,25)]
[(1,4),(3,10),(6,9),(7,13),(8,11),(12,18),(14,17),(15,22),(16,19),(21,24)]
[(2,6),(3,8),(5,7),(9,12),(13,16),(17,22),(18,20),(19,23)]
[(1,2),(4,6),(5,9),(7,10),(11,12),(13,14),(15,18),(16,20),(19,21),(23,24)]
[(2,4),(3,5),(7,13),(8,9),(10,14),(11,15),(12,18),(16,17),(20,22),(21,23)]
[(3,4),(6,9),(7,11),(10,12),(13,15),(14,18),(16,19),(21,22)]
[(5,7),(6,8),(9,13),(10,11),(12,16),(14,15),(17,19),(18,20)]
[(5,6),(7,8),(9,10),(11,13),(12,14),(15,16),(17,18),(19,20)]
[(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21)]

Improved size over 140 that could be obtained by Batcher odd-even merge with same depth
Sorting network for 26 inputs, 140 CEs, 14 layers:

[(0,25),(1,3),(2,9),(4,19),(5,18),(6,21),(7,20),(8,10),(11,12),(13,14),(15,17),(16,23),(22,24)]
[(1,4),(2,16),(3,19),(5,13),(6,22),(7,11),(8,15),(9,23),(10,17),(12,20),(14,18),(21,24)]
[(1,5),(2,8),(3,14),(4,13),(6,7),(9,15),(10,16),(11,22),(12,21),(17,23),(18,19),(20,24)]
[(0,9),(2,6),(5,12),(7,10),(13,20),(15,18),(16,25),(19,23)]
[(0,5),(3,12),(8,9),(13,22),(16,17),(20,25)]
[(0,1),(3,16),(4,8),(5,11),(9,22),(10,12),(13,15),(14,20),(17,21),(24,25)]
[(0,2),(1,6),(3,7),(4,5),(8,11),(9,15),(10,16),(14,17),(18,22),(19,24),(20,21),(23,25)]
[(1,3),(2,4),(5,7),(6,13),(8,14),(9,10),(11,17),(12,19),(15,16),(18,20),(21,23),(22,24)]
[(1,2),(3,4),(5,8),(6,9),(7,14),(10,13),(11,18),(12,15),(16,19),(17,20),(21,22),(23,24)]
[(2,3),(5,6),(7,11),(8,9),(10,12),(13,15),(14,18),(16,17),(19,20),(22,23)]
[(3,5),(4,9),(7,10),(11,12),(13,14),(15,18),(16,21),(20,22)]
[(4,8),(6,7),(9,13),(10,11),(12,16),(14,15),(17,21),(18,19)]
[(4,6),(7,8),(9,10),(11,13),(12,14),(15,16),(17,18),(19,21)]
[(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21)]

Improved size over 142 that could be obtained by Batcher odd-even merge with same depth
Sorting network for 26 inputs, 145 CEs, 13 layers:

[(0,13),(1,6),(2,8),(3,20),(4,7),(5,22),(9,16),(10,15),(11,14),(12,25),(17,23),(18,21),(19,24)]
[(0,3),(1,19),(4,18),(5,12),(6,24),(7,21),(8,16),(9,17),(10,11),(13,20),(14,15),(22,25)]
[(0,10),(1,5),(2,17),(3,12),(6,11),(7,16),(8,23),(9,18),(13,22),(14,19),(15,25),(20,24)]
[(0,1),(2,9),(3,14),(4,8),(5,10),(6,13),(7,18),(11,22),(12,19),(15,20),(16,23),(17,21),(24,25)]
[(1,5),(2,4),(3,6),(7,9),(8,17),(10,15),(11,14),(12,13),(16,18),(19,22),(20,24),(21,23)]
[(0,2),(1,3),(4,7),(5,6),(8,10),(9,16),(11,12),(13,14),(15,17),(18,21),(19,20),(22,24),(23,25)]
[(1,2),(3,4),(6,18),(7,19),(8,11),(9,12),(10,15),(13,16),(14,17),(21,22),(23,24)]
[(1,9),(2,11),(4,6),(5,7),(10,12),(13,15),(14,23),(16,24),(18,20),(19,21)]
[(1,3),(2,8),(6,14),(7,13),(9,10),(11,19),(12,18),(15,16),(17,23),(22,24)]
[(2,5),(4,9),(6,10),(7,8),(11,13),(12,14),(15,19),(16,21),(17,18),(20,23)]
[(3,5),(4,7),(6,11),(8,9),(10,12),(13,15),(14,19),(16,17),(18,21),(20,22)]
[(2,3),(5,7),(6,8),(9,11),(10,13),(12,15),(14,16),(17,19),(18,20),(22,23)]
[(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21)]

Improved depth that could be obtained by Batcher odd-even merge
Sorting network for 27 inputs, 150 CEs, 15 layers:

[(0,9),(1,6),(2,4),(3,7),(5,8),(11,24),(12,23),(13,26),(14,25),(15,19),(16,17),(18,22),(20,21)]
[(0,1),(3,5),(4,10),(6,9),(7,8),(11,16),(12,18),(13,20),(14,15),(17,24),(19,25),(21,26),(22,23)]
[(1,3),(2,5),(4,7),(8,10),(11,12),(13,14),(15,16),(17,19),(18,20),(21,22),(23,24),(25,26)]
[(0,4),(1,2),(3,7),(5,9),(6,8),(11,13),(12,14),(15,21),(16,22),(17,18),(19,20),(23,25),(24,26)]
[(0,1),(2,6),(4,5),(7,8),(9,10),(12,13),(14,23),(15,17),(16,18),(19,21),(20,22),(24,25)]
[(0,11),(2,4),(3,6),(5,7),(8,9),(12,15),(13,17),(16,19),(18,21),(20,24),(22,25)]
[(1,2),(3,4),(5,6),(7,8),(13,15),(14,17),(20,23),(22,24)]
[(1,12),(2,3),(4,5),(6,7),(14,16),(17,19),(18,20),(21,23)]
[(2,13),(14,15),(16,17),(18,19),(20,21),(22,23)]
[(3,14),(4,15),(5,16),(10,21),(17,18),(19,20)]
[(6,17),(7,18),(8,19),(9,20),(10,13),(14,22),(15,23),(16,24)]
[(6,10),(7,14),(8,11),(9,12),(17,25),(18,26),(19,23),(20,24)]
[(4,8),(5,9),(11,15),(12,16),(13,17),(18,22),(21,25),(24,26)]
[(2,4),(3,5),(6,8),(7,9),(10,11),(12,14),(13,15),(16,18),(17,19),(20,22),(21,23),(25,26)]
[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20),(21,22),(23,24)]

Batcher odd-even merge of smallest known networks with 11 and 16 inputs
Sorting network for 27 inputs, 151 CEs, 14 layers:

[(0,9),(1,6),(2,4),(3,7),(5,8),(11,16),(12,15),(13,23),(14,24),(17,18),(19,20),(21,26),(22,25)]
[(0,1),(3,5),(4,10),(6,9),(7,8),(11,13),(12,21),(14,17),(15,18),(16,25),(19,22),(20,23),(24,26)]
[(1,3),(2,5),(4,7),(8,10),(11,19),(12,14),(13,22),(15,24),(16,20),(17,21),(18,26),(23,25)]
[(0,4),(1,2),(3,7),(5,9),(6,8),(11,12),(13,15),(14,19),(16,17),(18,23),(20,21),(22,24),(25,26)]
[(0,1),(2,6),(4,5),(7,8),(9,10),(12,14),(13,16),(15,19),(17,20),(18,22),(21,24),(23,25)]
[(0,11),(2,4),(3,6),(5,7),(8,9),(12,13),(14,16),(15,22),(17,19),(18,20),(21,23),(24,25)]
[(1,2),(3,4),(5,6),(7,8),(13,14),(15,16),(17,18),(19,20),(21,22),(23,24)]
[(1,12),(2,3),(4,5),(6,7),(15,17),(16,18),(19,21),(20,22)]
[(2,13),(14,15),(16,17),(18,19),(20,21),(22,23)]
[(3,14),(4,15),(5,16),(6,17),(7,18),(8,19),(9,20),(10,21)]
[(8,11),(9,12),(10,13),(14,22),(15,23),(16,24),(17,25),(18,26)]
[(4,8),(5,9),(6,10),(7,14),(11,15),(12,16),(13,17),(18,22),(19,23),(20,24),(21,25)]
[(2,4),(3,5),(6,8),(7,9),(10,11),(12,14),(13,15),(16,18),(17,19),(20,22),(21,23),(24,26)]
[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20),(21,22),(23,24),(25,26)]

Batcher odd-even merge of 11 input network and 16 input network with 9 layers
Sorting network for 28 inputs, 155 CEs, 15 layers:

[(0,9),(1,20),(2,21),(3,22),(4,19),(5,24),(6,25),(7,26),(8,23),(10,15),(11,13),(12,17),(14,16),(18,27)]
[(0,18),(1,7),(2,6),(3,5),(4,8),(9,27),(10,12),(11,14),(13,16),(15,17),(19,23),(20,26),(21,25),(22,24)]
[(1,2),(3,4),(5,19),(6,20),(7,21),(8,22),(9,18),(10,11),(12,14),(13,15),(16,17),(23,24),(25,26)]
[(0,3),(1,10),(5,8),(6,7),(11,13),(14,16),(17,26),(19,22),(20,21),(24,27)]
[(0,1),(2,7),(3,10),(4,8),(12,13),(14,15),(17,24),(19,23),(20,25),(26,27)]
[(1,3),(2,6),(4,5),(7,19),(8,20),(11,12),(13,14),(15,16),(21,25),(22,23),(24,26)]
[(2,4),(5,12),(7,8),(9,11),(10,14),(13,17),(15,22),(16,18),(19,20),(23,25)]
[(2,9),(4,11),(5,6),(7,13),(8,10),(14,20),(16,23),(17,19),(18,25),(21,22)]
[(1,2),(3,16),(4,9),(6,12),(10,14),(11,24),(13,17),(15,21),(18,23),(25,26)]
[(2,8),(3,5),(4,7),(6,16),(9,15),(11,21),(12,18),(19,25),(20,23),(22,24)]
[(2,3),(5,8),(7,9),(11,15),(12,16),(18,20),(19,22),(24,25)]
[(6,8),(10,12),(11,13),(14,16),(15,17),(19,21)]
[(5,6),(8,10),(9,11),(12,13),(14,15),(16,18),(17,19),(21,22)]
[(4,5),(6,7),(8,9),(10,11),(12,14),(13,15),(16,17),(18,19),(20,21),(22,23)]
[(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20),(21,22),(23,24)]

Improved size over 156 that could be obtained by Batcher odd-even merge
Sorting network for 28 inputs, 157 CEs, 14 layers:

[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21),(22,23),(24,25),(26,27)]
[(0,26),(1,27),(2,24),(3,25),(4,22),(5,23),(6,20),(7,21),(8,18),(9,19),(10,16),(11,17),(12,14),(13,15)]
[(0,6),(1,20),(2,4),(3,5),(7,26),(10,12),(11,14),(13,16),(15,17),(21,27),(22,24),(23,25)]
[(1,18),(2,10),(4,22),(5,23),(6,8),(9,26),(12,13),(14,15),(17,25),(19,21)]
[(0,6),(3,22),(4,12),(5,24),(7,9),(11,13),(14,16),(15,23),(18,20),(21,27)]
[(0,2),(1,4),(3,11),(5,13),(6,10),(7,8),(14,22),(16,24),(17,21),(19,20),(23,26),(25,27)]
[(1,6),(3,7),(4,11),(5,10),(8,15),(9,14),(12,19),(13,18),(16,23),(17,22),(20,24),(21,26)]
[(2,9),(4,8),(5,13),(7,17),(10,20),(11,15),(12,16),(14,22),(18,25),(19,23)]
[(2,3),(4,5),(7,12),(8,11),(10,13),(14,17),(15,20),(16,19),(22,23),(24,25)]
[(1,2),(5,6),(8,10),(9,12),(11,14),(13,16),(15,18),(17,19),(21,22),(25,26)]
[(3,5),(6,9),(7,8),(10,12),(11,13),(14,16),(15,17),(18,21),(19,20),(22,24)]
[(2,3),(4,7),(5,6),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,23),(21,22),(24,25)]
[(4,5),(6,7),(8,10),(9,11),(12,14),(13,15),(16,18),(17,19),(20,21),(22,23)]
[(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20),(21,22),(23,24)]

Identical size and depth can be obtained by Batcher odd-even merge of 12 and 16 input networks with 9 layers each.
Sorting network for 29 inputs, 165 CEs, 15 layers:

[(0,12),(1,10),(2,9),(3,7),(5,11),(6,8),(13,26),(14,25),(15,28),(16,27),(17,21),(18,19),(20,24),(22,23)]
[(1,6),(2,3),(4,11),(7,9),(8,10),(13,18),(14,20),(15,22),(16,17),(19,26),(21,27),(23,28),(24,25)]
[(0,4),(1,2),(3,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,21),(20,22),(23,24),(25,26),(27,28)]
[(4,6),(5,9),(8,11),(10,12),(13,15),(14,16),(17,23),(18,24),(19,20),(21,22),(25,27),(26,28)]
[(0,5),(3,8),(4,7),(6,11),(9,10),(14,15),(16,25),(17,19),(18,20),(21,23),(22,24),(26,27)]
[(0,1),(2,5),(6,9),(7,8),(10,11),(14,17),(15,19),(18,21),(20,23),(22,26),(24,27)]
[(0,13),(1,3),(2,4),(5,6),(9,10),(15,17),(16,19),(22,25),(24,26)]
[(1,2),(3,4),(5,7),(6,8),(16,18),(19,21),(20,22),(23,25)]
[(1,14),(2,3),(4,5),(6,7),(8,9),(16,17),(18,19),(20,21),(22,23),(24,25)]
[(2,15),(3,4),(5,6),(10,23),(11,24),(12,25),(19,20),(21,22)]
[(3,16),(4,17),(5,18),(6,19),(7,20),(8,21),(9,22),(10,15)]
[(6,10),(8,13),(9,14),(11,16),(12,17),(18,26),(19,27),(20,28)]
[(4,8),(5,9),(7,11),(12,13),(14,18),(15,19),(16,20),(17,21),(22,26),(23,27),(24,28)]
[(2,4),(3,5),(6,8),(7,9),(10,12),(11,14),(13,15),(16,18),(17,19),(20,22),(21,23),(24,26),(25,27)]
[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20),(21,22),(23,24),(25,26),(27,28)]

Batcher odd-even merge of smallest known networks with 13 and 16 inputs. As remarked by GitHub user Morwenn (https://gist.github.com/Morwenn/b8c138edd50c035094c12884b340aa04), several literature references state a size of 166.
Sorting network for 29 inputs, 166 CEs, 14 layers:

[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21),(22,23),(24,25),(26,27)]
[(0,2),(1,3),(4,6),(5,7),(8,10),(9,11),(12,14),(13,15),(16,18),(17,19),(20,22),(21,23),(24,26),(25,27)]
[(0,4),(1,5),(2,6),(3,7),(8,12),(9,13),(10,14),(11,15),(16,20),(17,21),(18,22),(19,23),(24,28)]
[(0,8),(1,9),(2,10),(3,11),(4,12),(5,13),(6,14),(7,15),(16,24),(17,25),(18,26),(19,27),(20,28)]
[(0,16),(1,8),(2,4),(3,12),(5,10),(6,9),(7,14),(11,13),(17,24),(18,20),(19,28),(21,26),(22,25),(23,27)]
[(1,2),(3,5),(4,8),(6,22),(7,11),(9,25),(10,12),(13,14),(17,18),(19,21),(20,24),(26,28)]
[(1,17),(2,18),(3,19),(4,20),(5,10),(7,23),(8,24),(11,27),(12,28),(13,25),(21,26)]
[(3,17),(4,16),(5,21),(6,18),(7,9),(8,20),(10,26),(11,23),(14,28),(15,27),(22,24)]
[(1,4),(3,8),(5,16),(7,17),(9,21),(10,22),(11,19),(12,20),(14,24),(15,26),(23,28)]
[(2,5),(7,8),(9,18),(11,17),(12,16),(13,22),(14,20),(15,19),(23,24)]
[(2,4),(6,12),(9,16),(10,11),(13,17),(14,18),(15,22),(19,25),(20,21)]
[(5,6),(8,12),(9,10),(11,13),(14,16),(15,17),(18,20),(19,23),(21,22),(25,26)]
[(3,5),(6,7),(8,9),(10,12),(11,14),(13,16),(15,18),(17,20),(19,21),(22,23),(24,25),(26,28)]
[(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20),(21,22),(23,24),(25,26),(27,28)]

Obtained by removing 3 inputs from the 32 input network with 185 elements and 14 layers.
Sorting network for 30 inputs, 172 CEs, 15 layers:

[(1,2),(3,10),(4,14),(5,8),(6,13),(7,12),(9,11),(16,17),(18,25),(19,29),(20,23),(21,28),(22,27),(24,26)]
[(0,14),(1,5),(2,8),(3,7),(6,9),(10,12),(11,13),(15,29),(16,20),(17,23),(18,22),(21,24),(25,27),(26,28)]
[(0,7),(1,6),(2,9),(4,10),(5,11),(8,13),(12,14),(15,22),(16,21),(17,24),(19,25),(20,26),(23,28),(27,29)]
[(0,6),(2,4),(3,5),(7,11),(8,10),(9,12),(13,14),(15,21),(17,19),(18,20),(22,26),(23,25),(24,27),(28,29)]
[(0,3),(1,2),(4,7),(5,9),(6,8),(10,11),(12,13),(14,29),(15,18),(16,17),(19,22),(20,24),(21,23),(25,26),(27,28)]
[(0,1),(2,3),(4,6),(7,9),(10,12),(11,13),(15,16),(17,18),(19,21),(22,24),(25,27),(26,28)]
[(0,15),(1,2),(3,5),(8,10),(11,12),(13,28),(16,17),(18,20),(23,25),(26,27)]
[(1,16),(3,4),(5,6),(7,8),(9,10),(12,27),(18,19),(20,21),(22,23),(24,25)]
[(2,3),(4,5),(6,7),(8,9),(10,11),(17,18),(19,20),(21,22),(23,24),(25,26)]
[(2,17),(3,18),(4,19),(5,6),(7,8),(9,24),(10,25),(11,26),(20,21),(22,23)]
[(5,20),(6,21),(7,22),(8,23),(9,16),(10,17),(11,18),(12,19)]
[(5,9),(6,10),(7,11),(8,15),(13,20),(14,21),(18,22),(19,23)]
[(3,5),(4,8),(7,9),(12,15),(13,16),(14,17),(20,24),(21,25)]
[(2,4),(6,8),(10,12),(11,13),(14,15),(16,18),(17,19),(20,22),(21,23),(24,26),(25,27)]
[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20),(21,22),(23,24),(25,26),(27,28)]

Batcher odd-even merge of twice the smallest known network with 15 inputs
Sorting network for 30 inputs, 173 CEs, 14 layers:

[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21),(22,23),(24,25),(26,27),(28,29)]
[(0,2),(1,3),(4,6),(5,7),(8,10),(9,11),(12,14),(13,15),(16,18),(17,19),(20,22),(21,23),(24,26),(25,27)]
[(0,4),(1,5),(2,6),(3,7),(8,12),(9,13),(10,14),(11,15),(16,20),(17,21),(18,22),(19,23),(24,28),(25,29)]
[(0,8),(1,9),(2,10),(3,11),(4,12),(5,13),(6,14),(7,15),(16,24),(17,25),(18,26),(19,27),(20,28),(21,29)]
[(0,16),(1,8),(2,4),(3,12),(5,10),(6,9),(7,14),(11,13),(17,24),(18,20),(19,28),(21,26),(22,25),(27,29)]
[(1,2),(3,5),(4,8),(6,22),(7,11),(9,25),(10,12),(13,14),(17,18),(19,21),(20,24),(23,27),(26,28)]
[(1,17),(2,18),(3,19),(4,20),(5,10),(7,23),(8,24),(11,27),(12,28),(13,29),(21,26)]
[(3,17),(4,16),(5,21),(6,18),(7,9),(8,20),(10,26),(11,23),(13,25),(14,28),(15,27),(22,24)]
[(1,4),(3,8),(5,16),(7,17),(9,21),(10,22),(11,19),(12,20),(14,24),(15,26),(23,28)]
[(2,5),(7,8),(9,18),(11,17),(12,16),(13,22),(14,20),(15,19),(23,24),(26,29)]
[(2,4),(6,12),(9,16),(10,11),(13,17),(14,18),(15,22),(19,25),(20,21),(27,29)]
[(5,6),(8,12),(9,10),(11,13),(14,16),(15,17),(18,20),(19,23),(21,22),(25,26)]
[(3,5),(6,7),(8,9),(10,12),(11,14),(13,16),(15,18),(17,20),(19,21),(22,23),(24,25),(26,28)]
[(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20),(21,22),(23,24),(25,26),(27,28)]

Obtained by removing 2 inputs from the 32 input network with 185 elements and 14 layers.
Sorting network for 31 inputs, 180 CEs, 14 layers:

[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21),(22,23),(24,25),(26,27),(28,29)]
[(0,2),(1,3),(4,6),(5,7),(8,10),(9,11),(12,14),(13,15),(16,18),(17,19),(20,22),(21,23),(24,26),(25,27),(28,30)]
[(0,4),(1,5),(2,6),(3,7),(8,12),(9,13),(10,14),(11,15),(16,20),(17,21),(18,22),(19,23),(24,28),(25,29),(26,30)]
[(0,8),(1,9),(2,10),(3,11),(4,12),(5,13),(6,14),(7,15),(16,24),(17,25),(18,26),(19,27),(20,28),(21,29),(22,30)]
[(0,16),(1,8),(2,4),(3,12),(5,10),(6,9),(7,14),(11,13),(17,24),(18,20),(19,28),(21,26),(22,25),(23,30),(27,29)]
[(1,2),(3,5),(4,8),(6,22),(7,11),(9,25),(10,12),(13,14),(17,18),(19,21),(20,24),(23,27),(26,28),(29,30)]
[(1,17),(2,18),(3,19),(4,20),(5,10),(7,23),(8,24),(11,27),(12,28),(13,29),(14,30),(21,26)]
[(3,17),(4,16),(5,21),(6,18),(7,9),(8,20),(10,26),(11,23),(13,25),(14,28),(15,27),(22,24)]
[(1,4),(3,8),(5,16),(7,17),(9,21),(10,22),(11,19),(12,20),(14,24),(15,26),(23,28),(27,30)]
[(2,5),(7,8),(9,18),(11,17),(12,16),(13,22),(14,20),(15,19),(23,24),(26,29)]
[(2,4),(6,12),(9,16),(10,11),(13,17),(14,18),(15,22),(19,25),(20,21),(27,29)]
[(5,6),(8,12),(9,10),(11,13),(14,16),(15,17),(18,20),(19,23),(21,22),(25,26)]
[(3,5),(6,7),(8,9),(10,12),(11,14),(13,16),(15,18),(17,20),(19,21),(22,23),(24,25),(26,28)]
[(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20),(21,22),(23,24),(25,26),(27,28)]

Obtained by removing one input from the network with 32 inputs, 185 elements and 14 layers. Its size and depth combine the best results that can be achieved using a Batcher odd-even merge of either twice the 15 input network with 56 CEs and 10 layers or twice the 15 input network with 57 CEs and 9 layers.