[[90,20,7]] · QEC Challenge

[[90,20,7]] d =

kd²/n

10.889

X/Z

Share this result

Distance

X/Z asymmetry 1 · d_X = 7, d_Z = 7 · w_X = 31, w_Z = 31 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)

d_X 7 · witness weight 7 (claimed upper_bound)

witness operator (support, 7 qubits)

[19, 20, 27, 28, 49, 58, 73]

d_Z 7 · witness weight 7 (claimed upper_bound)

witness operator (support, 7 qubits)

[18, 33, 42, 63, 64, 71, 72]

certificate exact, d = 7 · CryptoMiniSat 5.14.7 SAT

X: no logical < 7 exists; Z: no logical < 7 exists

Diagnostics

computed by the verifier from the parity checks, the layout, and the stored witnesses; shown as evidence, not used for ranking

girth H_X 4 · H_Z 4 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)

check weights H_X 31 · H_Z 31

qubit degrees H_X 12–19 (mean 15.5) · H_Z 12–19 (mean 15.5)

trapping sets H_X (1,12)×45 (2,12)×135 (3,4)×45 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

full (size, syndrome weight): count census for H_X

(1,12): 45 (1,19): 45 (2,12): 135 (2,14): 90 (2,15): 45 (2,16): 270 (2,17): 270 (2,18): 180 (2,19): 585 (2,20): 315 (2,21): 315 (2,22): 450 (2,23): 585 (2,24): 225 (2,25): 135 (2,26): 135 (2,27): 90 (2,28): 45 (3,4): 45 (3,10): 135 (3,12): 540 (3,13): 270 (3,14): 1080 (3,15): 1575 (3,16): 2655 (3,17): 4725 (3,18): 5625 (3,19): 9405 (3,20): 9090 (3,21): 14145 (3,22): 15480 (3,23): 13095 (3,24): 12795 (3,25): 8730 (3,26): 7740 (3,27): 4680 (3,28): 2295 (3,29): 1440 (3,30): 540 (3,31): 270 (3,32): 45 (3,33): 360 (3,37): 45

trapping sets H_Z (1,12)×45 (2,12)×135 (3,4)×45 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

full (size, syndrome weight): count census for H_Z

Construction & provenance

authors Liangdong Lu and Guanmin Guo and Yang Liu and Ruipan Yang and @mathysrennela

provenance submitted through the challenge

novelty known parameter set; see provenance notes

construction Cyclic bicycle over F_2[Z_45], with circulant supports a=[0, 1, 3, 5, 7, 8, 9, 10, 36, 39, 40, 42] and b=[0, 1, 2, 4, 5, 8, 10, 21, 22, 23, 25, 26, 29, 30, 32, 34, 35, 38, 40], from Table III of arXiv:2608.09115v1.

model GPT-5.6 Luna (claimed, not verified)

builds on arXiv:2608.09115

date 2026-08-10

notes The paper reports exact d=7. This staged record keeps the repository's witness-backed distance evidence as upper_bound until trusted certification.

family generalized bicycle (a tag, not a ranking)

locality unrestricted (computed from the layout)

weight class weight > 8 (computed)

How this code was found

the research note submitted with this code · raw markdown · all notes

[[90,20,7]] — cyclic bicycle reconstruction from arXiv:2608.09115v1

Direction & hypothesis

This is a direct reconstruction of the explicit cyclic bicycle row in Table III of arXiv:2608.09115v1. The paper reports [[90,20,7]] with exact distance 7. The candidate was checked against the unrestricted weight-capable board cell before submission and advances that cell.

What was searched

No new search was performed. The published cyclic supports were assembled over F_2[Z_45] as H_X = [A|B] and H_Z = [B^T|A^T]. The support sets are supp(a) = {0,1,3,5,7,8,9,10,36,39,40,42} and supp(b) = {0,1,2,4,5,8,10,21,22,23,25,26,29,30,32,34,35,38,40}.

Evidence trail

The reconstructed matrices have n=90, k=20, CSS commutation, and maximum check weight 31. The repository submission builder preserved explicit X- and Z-side logical witnesses. verify/validate_candidate.py returned passed: true, with no exact or WL-equivalent board duplicate and board_advancing: true. The staged record therefore uses witness-backed upper_bound confidence. The paper's exact d=7 claim is reported as provenance, not converted into repository exact certification.

Dead ends

The paper's [[90,18,8]] row reconstructs with raw maximum check weight 38 and is outside the repository cap of 32; it was not submitted.

Tools

Model: GPT-5.6 Luna. Repository tooling: research/kit/bb.py, research/kit/css.py, research/kit/submit.py, and verify/validate_candidate.py. Author: @mathysrennela.

Reproduction

Use the support sets above with the cyclic specialization of the two-block bicycle construction over Z_45. The immutable source is arXiv:2608.09115v1, Table III.

Parity checks

X-checks 45 (max weight 31) · Z-checks 45 (max weight 31)

H_X (45 checks, sparse supports)

[0, 1, 3, 5, 7, 8, 9, 10, 36, 39, 40, 42, 45, 46, 47, 49, 50, 53, 55, 66, 67, 68, 70, 71, 74, 75, 77, 79, 80, 83, 85] [1, 2, 4, 6, 8, 9, 10, 11, 37, 40, 41, 43, 46, 47, 48, 50, 51, 54, 56, 67, 68, 69, 71, 72, 75, 76, 78, 80, 81, 84, 86] [2, 3, 5, 7, 9, 10, 11, 12, 38, 41, 42, 44, 47, 48, 49, 51, 52, 55, 57, 68, 69, 70, 72, 73, 76, 77, 79, 81, 82, 85, 87] [0, 3, 4, 6, 8, 10, 11, 12, 13, 39, 42, 43, 48, 49, 50, 52, 53, 56, 58, 69, 70, 71, 73, 74, 77, 78, 80, 82, 83, 86, 88] [1, 4, 5, 7, 9, 11, 12, 13, 14, 40, 43, 44, 49, 50, 51, 53, 54, 57, 59, 70, 71, 72, 74, 75, 78, 79, 81, 83, 84, 87, 89] [0, 2, 5, 6, 8, 10, 12, 13, 14, 15, 41, 44, 45, 50, 51, 52, 54, 55, 58, 60, 71, 72, 73, 75, 76, 79, 80, 82, 84, 85, 88] [0, 1, 3, 6, 7, 9, 11, 13, 14, 15, 16, 42, 46, 51, 52, 53, 55, 56, 59, 61, 72, 73, 74, 76, 77, 80, 81, 83, 85, 86, 89] [1, 2, 4, 7, 8, 10, 12, 14, 15, 16, 17, 43, 45, 47, 52, 53, 54, 56, 57, 60, 62, 73, 74, 75, 77, 78, 81, 82, 84, 86, 87] [2, 3, 5, 8, 9, 11, 13, 15, 16, 17, 18, 44, 46, 48, 53, 54, 55, 57, 58, 61, 63, 74, 75, 76, 78, 79, 82, 83, 85, 87, 88] [0, 3, 4, 6, 9, 10, 12, 14, 16, 17, 18, 19, 47, 49, 54, 55, 56, 58, 59, 62, 64, 75, 76, 77, 79, 80, 83, 84, 86, 88, 89] [1, 4, 5, 7, 10, 11, 13, 15, 17, 18, 19, 20, 45, 48, 50, 55, 56, 57, 59, 60, 63, 65, 76, 77, 78, 80, 81, 84, 85, 87, 89] [2, 5, 6, 8, 11, 12, 14, 16, 18, 19, 20, 21, 45, 46, 49, 51, 56, 57, 58, 60, 61, 64, 66, 77, 78, 79, 81, 82, 85, 86, 88] [3, 6, 7, 9, 12, 13, 15, 17, 19, 20, 21, 22, 46, 47, 50, 52, 57, 58, 59, 61, 62, 65, 67, 78, 79, 80, 82, 83, 86, 87, 89] [4, 7, 8, 10, 13, 14, 16, 18, 20, 21, 22, 23, 45, 47, 48, 51, 53, 58, 59, 60, 62, 63, 66, 68, 79, 80, 81, 83, 84, 87, 88] [5, 8, 9, 11, 14, 15, 17, 19, 21, 22, 23, 24, 46, 48, 49, 52, 54, 59, 60, 61, 63, 64, 67, 69, 80, 81, 82, 84, 85, 88, 89] [6, 9, 10, 12, 15, 16, 18, 20, 22, 23, 24, 25, 45, 47, 49, 50, 53, 55, 60, 61, 62, 64, 65, 68, 70, 81, 82, 83, 85, 86, 89] [7, 10, 11, 13, 16, 17, 19, 21, 23, 24, 25, 26, 45, 46, 48, 50, 51, 54, 56, 61, 62, 63, 65, 66, 69, 71, 82, 83, 84, 86, 87] [8, 11, 12, 14, 17, 18, 20, 22, 24, 25, 26, 27, 46, 47, 49, 51, 52, 55, 57, 62, 63, 64, 66, 67, 70, 72, 83, 84, 85, 87, 88] [9, 12, 13, 15, 18, 19, 21, 23, 25, 26, 27, 28, 47, 48, 50, 52, 53, 56, 58, 63, 64, 65, 67, 68, 71, 73, 84, 85, 86, 88, 89] [10, 13, 14, 16, 19, 20, 22, 24, 26, 27, 28, 29, 45, 48, 49, 51, 53, 54, 57, 59, 64, 65, 66, 68, 69, 72, 74, 85, 86, 87, 89] [11, 14, 15, 17, 20, 21, 23, 25, 27, 28, 29, 30, 45, 46, 49, 50, 52, 54, 55, 58, 60, 65, 66, 67, 69, 70, 73, 75, 86, 87, 88] [12, 15, 16, 18, 21, 22, 24, 26, 28, 29, 30, 31, 46, 47, 50, 51, 53, 55, 56, 59, 61, 66, 67, 68, 70, 71, 74, 76, 87, 88, 89] [13, 16, 17, 19, 22, 23, 25, 27, 29, 30, 31, 32, 45, 47, 48, 51, 52, 54, 56, 57, 60, 62, 67, 68, 69, 71, 72, 75, 77, 88, 89] [14, 17, 18, 20, 23, 24, 26, 28, 30, 31, 32, 33, 45, 46, 48, 49, 52, 53, 55, 57, 58, 61, 63, 68, 69, 70, 72, 73, 76, 78, 89] [15, 18, 19, 21, 24, 25, 27, 29, 31, 32, 33, 34, 45, 46, 47, 49, 50, 53, 54, 56, 58, 59, 62, 64, 69, 70, 71, 73, 74, 77, 79] [16, 19, 20, 22, 25, 26, 28, 30, 32, 33, 34, 35, 46, 47, 48, 50, 51, 54, 55, 57, 59, 60, 63, 65, 70, 71, 72, 74, 75, 78, 80] [17, 20, 21, 23, 26, 27, 29, 31, 33, 34, 35, 36, 47, 48, 49, 51, 52, 55, 56, 58, 60, 61, 64, 66, 71, 72, 73, 75, 76, 79, 81] [18, 21, 22, 24, 27, 28, 30, 32, 34, 35, 36, 37, 48, 49, 50, 52, 53, 56, 57, 59, 61, 62, 65, 67, 72, 73, 74, 76, 77, 80, 82] [19, 22, 23, 25, 28, 29, 31, 33, 35, 36, 37, 38, 49, 50, 51, 53, 54, 57, 58, 60, 62, 63, 66, 68, 73, 74, 75, 77, 78, 81, 83] [20, 23, 24, 26, 29, 30, 32, 34, 36, 37, 38, 39, 50, 51, 52, 54, 55, 58, 59, 61, 63, 64, 67, 69, 74, 75, 76, 78, 79, 82, 84] [21, 24, 25, 27, 30, 31, 33, 35, 37, 38, 39, 40, 51, 52, 53, 55, 56, 59, 60, 62, 64, 65, 68, 70, 75, 76, 77, 79, 80, 83, 85] [22, 25, 26, 28, 31, 32, 34, 36, 38, 39, 40, 41, 52, 53, 54, 56, 57, 60, 61, 63, 65, 66, 69, 71, 76, 77, 78, 80, 81, 84, 86] [23, 26, 27, 29, 32, 33, 35, 37, 39, 40, 41, 42, 53, 54, 55, 57, 58, 61, 62, 64, 66, 67, 70, 72, 77, 78, 79, 81, 82, 85, 87] [24, 27, 28, 30, 33, 34, 36, 38, 40, 41, 42, 43, 54, 55, 56, 58, 59, 62, 63, 65, 67, 68, 71, 73, 78, 79, 80, 82, 83, 86, 88] [25, 28, 29, 31, 34, 35, 37, 39, 41, 42, 43, 44, 55, 56, 57, 59, 60, 63, 64, 66, 68, 69, 72, 74, 79, 80, 81, 83, 84, 87, 89] [0, 26, 29, 30, 32, 35, 36, 38, 40, 42, 43, 44, 45, 56, 57, 58, 60, 61, 64, 65, 67, 69, 70, 73, 75, 80, 81, 82, 84, 85, 88] [0, 1, 27, 30, 31, 33, 36, 37, 39, 41, 43, 44, 46, 57, 58, 59, 61, 62, 65, 66, 68, 70, 71, 74, 76, 81, 82, 83, 85, 86, 89] [0, 1, 2, 28, 31, 32, 34, 37, 38, 40, 42, 44, 45, 47, 58, 59, 60, 62, 63, 66, 67, 69, 71, 72, 75, 77, 82, 83, 84, 86, 87] [0, 1, 2, 3, 29, 32, 33, 35, 38, 39, 41, 43, 46, 48, 59, 60, 61, 63, 64, 67, 68, 70, 72, 73, 76, 78, 83, 84, 85, 87, 88] [1, 2, 3, 4, 30, 33, 34, 36, 39, 40, 42, 44, 47, 49, 60, 61, 62, 64, 65, 68, 69, 71, 73, 74, 77, 79, 84, 85, 86, 88, 89] [0, 2, 3, 4, 5, 31, 34, 35, 37, 40, 41, 43, 45, 48, 50, 61, 62, 63, 65, 66, 69, 70, 72, 74, 75, 78, 80, 85, 86, 87, 89] [1, 3, 4, 5, 6, 32, 35, 36, 38, 41, 42, 44, 45, 46, 49, 51, 62, 63, 64, 66, 67, 70, 71, 73, 75, 76, 79, 81, 86, 87, 88] [0, 2, 4, 5, 6, 7, 33, 36, 37, 39, 42, 43, 46, 47, 50, 52, 63, 64, 65, 67, 68, 71, 72, 74, 76, 77, 80, 82, 87, 88, 89] [1, 3, 5, 6, 7, 8, 34, 37, 38, 40, 43, 44, 45, 47, 48, 51, 53, 64, 65, 66, 68, 69, 72, 73, 75, 77, 78, 81, 83, 88, 89] [0, 2, 4, 6, 7, 8, 9, 35, 38, 39, 41, 44, 45, 46, 48, 49, 52, 54, 65, 66, 67, 69, 70, 73, 74, 76, 78, 79, 82, 84, 89]

H_Z (45 checks, sparse supports)

[0, 5, 7, 10, 11, 13, 15, 16, 19, 20, 22, 23, 24, 35, 37, 40, 41, 43, 44, 45, 48, 50, 51, 54, 80, 81, 82, 83, 85, 87, 89] [0, 1, 6, 8, 11, 12, 14, 16, 17, 20, 21, 23, 24, 25, 36, 38, 41, 42, 44, 45, 46, 49, 51, 52, 55, 81, 82, 83, 84, 86, 88] [0, 1, 2, 7, 9, 12, 13, 15, 17, 18, 21, 22, 24, 25, 26, 37, 39, 42, 43, 46, 47, 50, 52, 53, 56, 82, 83, 84, 85, 87, 89] [1, 2, 3, 8, 10, 13, 14, 16, 18, 19, 22, 23, 25, 26, 27, 38, 40, 43, 44, 45, 47, 48, 51, 53, 54, 57, 83, 84, 85, 86, 88] [0, 2, 3, 4, 9, 11, 14, 15, 17, 19, 20, 23, 24, 26, 27, 28, 39, 41, 44, 46, 48, 49, 52, 54, 55, 58, 84, 85, 86, 87, 89] [0, 1, 3, 4, 5, 10, 12, 15, 16, 18, 20, 21, 24, 25, 27, 28, 29, 40, 42, 45, 47, 49, 50, 53, 55, 56, 59, 85, 86, 87, 88] [1, 2, 4, 5, 6, 11, 13, 16, 17, 19, 21, 22, 25, 26, 28, 29, 30, 41, 43, 46, 48, 50, 51, 54, 56, 57, 60, 86, 87, 88, 89] [2, 3, 5, 6, 7, 12, 14, 17, 18, 20, 22, 23, 26, 27, 29, 30, 31, 42, 44, 45, 47, 49, 51, 52, 55, 57, 58, 61, 87, 88, 89] [0, 3, 4, 6, 7, 8, 13, 15, 18, 19, 21, 23, 24, 27, 28, 30, 31, 32, 43, 45, 46, 48, 50, 52, 53, 56, 58, 59, 62, 88, 89] [1, 4, 5, 7, 8, 9, 14, 16, 19, 20, 22, 24, 25, 28, 29, 31, 32, 33, 44, 45, 46, 47, 49, 51, 53, 54, 57, 59, 60, 63, 89] [0, 2, 5, 6, 8, 9, 10, 15, 17, 20, 21, 23, 25, 26, 29, 30, 32, 33, 34, 45, 46, 47, 48, 50, 52, 54, 55, 58, 60, 61, 64] [1, 3, 6, 7, 9, 10, 11, 16, 18, 21, 22, 24, 26, 27, 30, 31, 33, 34, 35, 46, 47, 48, 49, 51, 53, 55, 56, 59, 61, 62, 65] [2, 4, 7, 8, 10, 11, 12, 17, 19, 22, 23, 25, 27, 28, 31, 32, 34, 35, 36, 47, 48, 49, 50, 52, 54, 56, 57, 60, 62, 63, 66] [3, 5, 8, 9, 11, 12, 13, 18, 20, 23, 24, 26, 28, 29, 32, 33, 35, 36, 37, 48, 49, 50, 51, 53, 55, 57, 58, 61, 63, 64, 67] [4, 6, 9, 10, 12, 13, 14, 19, 21, 24, 25, 27, 29, 30, 33, 34, 36, 37, 38, 49, 50, 51, 52, 54, 56, 58, 59, 62, 64, 65, 68] [5, 7, 10, 11, 13, 14, 15, 20, 22, 25, 26, 28, 30, 31, 34, 35, 37, 38, 39, 50, 51, 52, 53, 55, 57, 59, 60, 63, 65, 66, 69] [6, 8, 11, 12, 14, 15, 16, 21, 23, 26, 27, 29, 31, 32, 35, 36, 38, 39, 40, 51, 52, 53, 54, 56, 58, 60, 61, 64, 66, 67, 70] [7, 9, 12, 13, 15, 16, 17, 22, 24, 27, 28, 30, 32, 33, 36, 37, 39, 40, 41, 52, 53, 54, 55, 57, 59, 61, 62, 65, 67, 68, 71] [8, 10, 13, 14, 16, 17, 18, 23, 25, 28, 29, 31, 33, 34, 37, 38, 40, 41, 42, 53, 54, 55, 56, 58, 60, 62, 63, 66, 68, 69, 72] [9, 11, 14, 15, 17, 18, 19, 24, 26, 29, 30, 32, 34, 35, 38, 39, 41, 42, 43, 54, 55, 56, 57, 59, 61, 63, 64, 67, 69, 70, 73] [10, 12, 15, 16, 18, 19, 20, 25, 27, 30, 31, 33, 35, 36, 39, 40, 42, 43, 44, 55, 56, 57, 58, 60, 62, 64, 65, 68, 70, 71, 74] [0, 11, 13, 16, 17, 19, 20, 21, 26, 28, 31, 32, 34, 36, 37, 40, 41, 43, 44, 56, 57, 58, 59, 61, 63, 65, 66, 69, 71, 72, 75] [0, 1, 12, 14, 17, 18, 20, 21, 22, 27, 29, 32, 33, 35, 37, 38, 41, 42, 44, 57, 58, 59, 60, 62, 64, 66, 67, 70, 72, 73, 76] [0, 1, 2, 13, 15, 18, 19, 21, 22, 23, 28, 30, 33, 34, 36, 38, 39, 42, 43, 58, 59, 60, 61, 63, 65, 67, 68, 71, 73, 74, 77] [1, 2, 3, 14, 16, 19, 20, 22, 23, 24, 29, 31, 34, 35, 37, 39, 40, 43, 44, 59, 60, 61, 62, 64, 66, 68, 69, 72, 74, 75, 78] [0, 2, 3, 4, 15, 17, 20, 21, 23, 24, 25, 30, 32, 35, 36, 38, 40, 41, 44, 60, 61, 62, 63, 65, 67, 69, 70, 73, 75, 76, 79] [0, 1, 3, 4, 5, 16, 18, 21, 22, 24, 25, 26, 31, 33, 36, 37, 39, 41, 42, 61, 62, 63, 64, 66, 68, 70, 71, 74, 76, 77, 80] [1, 2, 4, 5, 6, 17, 19, 22, 23, 25, 26, 27, 32, 34, 37, 38, 40, 42, 43, 62, 63, 64, 65, 67, 69, 71, 72, 75, 77, 78, 81] [2, 3, 5, 6, 7, 18, 20, 23, 24, 26, 27, 28, 33, 35, 38, 39, 41, 43, 44, 63, 64, 65, 66, 68, 70, 72, 73, 76, 78, 79, 82] [0, 3, 4, 6, 7, 8, 19, 21, 24, 25, 27, 28, 29, 34, 36, 39, 40, 42, 44, 64, 65, 66, 67, 69, 71, 73, 74, 77, 79, 80, 83] [0, 1, 4, 5, 7, 8, 9, 20, 22, 25, 26, 28, 29, 30, 35, 37, 40, 41, 43, 65, 66, 67, 68, 70, 72, 74, 75, 78, 80, 81, 84] [1, 2, 5, 6, 8, 9, 10, 21, 23, 26, 27, 29, 30, 31, 36, 38, 41, 42, 44, 66, 67, 68, 69, 71, 73, 75, 76, 79, 81, 82, 85] [0, 2, 3, 6, 7, 9, 10, 11, 22, 24, 27, 28, 30, 31, 32, 37, 39, 42, 43, 67, 68, 69, 70, 72, 74, 76, 77, 80, 82, 83, 86] [1, 3, 4, 7, 8, 10, 11, 12, 23, 25, 28, 29, 31, 32, 33, 38, 40, 43, 44, 68, 69, 70, 71, 73, 75, 77, 78, 81, 83, 84, 87] [0, 2, 4, 5, 8, 9, 11, 12, 13, 24, 26, 29, 30, 32, 33, 34, 39, 41, 44, 69, 70, 71, 72, 74, 76, 78, 79, 82, 84, 85, 88] [0, 1, 3, 5, 6, 9, 10, 12, 13, 14, 25, 27, 30, 31, 33, 34, 35, 40, 42, 70, 71, 72, 73, 75, 77, 79, 80, 83, 85, 86, 89] [1, 2, 4, 6, 7, 10, 11, 13, 14, 15, 26, 28, 31, 32, 34, 35, 36, 41, 43, 45, 71, 72, 73, 74, 76, 78, 80, 81, 84, 86, 87] [2, 3, 5, 7, 8, 11, 12, 14, 15, 16, 27, 29, 32, 33, 35, 36, 37, 42, 44, 46, 72, 73, 74, 75, 77, 79, 81, 82, 85, 87, 88] [0, 3, 4, 6, 8, 9, 12, 13, 15, 16, 17, 28, 30, 33, 34, 36, 37, 38, 43, 47, 73, 74, 75, 76, 78, 80, 82, 83, 86, 88, 89] [1, 4, 5, 7, 9, 10, 13, 14, 16, 17, 18, 29, 31, 34, 35, 37, 38, 39, 44, 45, 48, 74, 75, 76, 77, 79, 81, 83, 84, 87, 89] [0, 2, 5, 6, 8, 10, 11, 14, 15, 17, 18, 19, 30, 32, 35, 36, 38, 39, 40, 45, 46, 49, 75, 76, 77, 78, 80, 82, 84, 85, 88] [1, 3, 6, 7, 9, 11, 12, 15, 16, 18, 19, 20, 31, 33, 36, 37, 39, 40, 41, 46, 47, 50, 76, 77, 78, 79, 81, 83, 85, 86, 89] [2, 4, 7, 8, 10, 12, 13, 16, 17, 19, 20, 21, 32, 34, 37, 38, 40, 41, 42, 45, 47, 48, 51, 77, 78, 79, 80, 82, 84, 86, 87] [3, 5, 8, 9, 11, 13, 14, 17, 18, 20, 21, 22, 33, 35, 38, 39, 41, 42, 43, 46, 48, 49, 52, 78, 79, 80, 81, 83, 85, 87, 88] [4, 6, 9, 10, 12, 14, 15, 18, 19, 21, 22, 23, 34, 36, 39, 40, 42, 43, 44, 47, 49, 50, 53, 79, 80, 81, 82, 84, 86, 88, 89]

Code ID 90-20-7 · download JSON · raw on GitHub