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[[254,72,17]] d ≤
n
254
k
72
d
17
kd²/n
81.921
w
16
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 17, d_Z ≤ 17 · w_X = 16, w_Z = 16 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 17 · witness weight 17 (claimed upper_bound)
witness operator (support, 17 qubits)
[4, 23, 52, 53, 87, 105, 111, 112, 143, 153, 164, 179, 185, 200, 222, 244, 247]
d_Z 17 · witness weight 17 (claimed upper_bound)
witness operator (support, 17 qubits)
[20, 32, 42, 67, 75, 90, 110, 118, 128, 138, 163, 168, 174, 232, 242, 247, 251]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

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 16 · H_Z 16
qubit degrees H_X 8 · H_Z 8
trapping sets H_X (1,8)×254 (2,12)×2032 (3,12)×254 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,8): 254 (2,12): 2032 (2,14): 11176 (3,12): 254 (3,14): 4699 (3,16): 54737 (3,18): 277368 (3,20): 581533 (3,22): 27559
trapping sets H_Z (1,8)×254 (2,12)×2032 (3,12)×254 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,8): 254 (2,12): 2032 (2,14): 11176 (3,12): 254 (3,14): 4699 (3,16): 54737 (3,18): 277368 (3,20): 581533 (3,22): 27559

Construction & provenance

authors @mathysrennela
provenance submitted through the challenge
novelty novelty not audited
construction Cyclic generalized bicycle over Z_127 (n=2m=254): H_X=[circ(a)|circ(b)], H_Z=[circ(b)^T|circ(a)^T]. a and b are sparse multiples of the BCH-designed divisor g(x) of x^m-1 (g_int=54066391421; zero-set run 3, complement run 8), found by Prange search inside the ideal (g). Zero-set design after arXiv:2609.22503 (BCH run-length floors); construction family per arXiv:1904.02703. a=[8, 29, 33, 37, 61, 76, 98, 109]; b=[1, 7, 42, 61, 85, 114, 124, 125].
model GLM 5.3 Flash (Zed agent) (claimed, not verified)
date 2026-09-22
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

[[254,72,17]] — BCH-designed cyclic generalized bicycle over Z_127

Direction & hypothesis

Target cell: unrestricted / any-weight (the code has no 2D layout; its combinatorial locality is not the board's geometric locality). Family: cyclic generalized bicycle over Z_127 (arXiv:1904.02703), the family that produced the board's top kd^2/n codes at n ~ 670-680. The opening this campaign aimed at: choose the common divisor g(x) of x^127-1 by its zero-set structure rather than uniformly, a defining-set idea transferred from arXiv:2609.22503 (optimal dual-containing cyclic LRCs). That paper's q-ary families cannot be binary (their Euclidean case needs (r+delta-1) | (q-1), impossible at q = 2), but one ingredient transfers provably: by the BCH bound, every nonzero multiple of g has Hamming weight >= s+1, where s is the longest run of consecutive exponents in the zero set Z(g) = {i : g(w^i) = 0}. The sparse cofactors h_a = a/g and h_b = b/g are exactly such multiples, so the run length is a zero-cost feasibility filter: an ideal whose zero set contains a run of length >= the target cofactor weight cannot yield a sparse cofactor at all, and the Prange search can be skipped entirely. Dually (Lemma 2.2 there), a run of length t in the complement of Z(gcd(b, x^m-1)) floors every pure-type X-logical (c, 0) in ker(B) at t+1; that complement run (8 here) was used only as a ranking prior, never as a distance claim.

What was searched

One sweep over divisor ideals of x^m - 1 for m in {127, 251, 257, 331, 337} (n = 2m in 254..674), degree targets matched to k = 2 deg(g) bands, cofactor weight band 4-9 (check weight <= 18). Ideals were enumerated as products of irreducible factors of x^m - 1; each ideal's zero set was computed exactly by evaluating g at the m-th roots of unity in GF(2^e) (e = ord_m(2), carryless arithmetic), and ideals whose zero-run exceeded the band were pruned before any search ran. Surviving ideals got a 4000-trial Prange search for sparse cofactors; pairs of cofactors built cyclic GB codes (H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T]), screened at 1200 RIS trials/side, and every screen-surviving code that was nondominated against the full board was deep-confirmed at 100,000 RIS trials/side. 29 records were staged; the 10 mutually non-dominating ones are being submitted, this code among them. The sweep took ~92 min wall clock; the zero-run filter pruned all k = 126/168 cells and all of m in {251, 257, 331} (coset degrees 50/16/30 do not match the swept degree grid) without spending a single search trial on them.

Evidence trail

Ladder for this code: screen 1200 trials/side -> deep confirm 100,000 trials/side -> d <= 17; the submission's own witness search (20,000 RIS trials/side plus a 1,000,000-trial gf2_fast accelerator pass, seed 0) returned the claimed bound d <= 17, with an explicit witness on each side recorded in the submission JSON. The claim is a witness-backed upper bound, not an exact distance; the trusted gate (verify/validate_candidate.py via ./qldpc submit) passed it locally, and CI re-runs the refutation with a fresh seed. Screen values at 1200 trials ran ~5-8% above the 100k deep values (e.g. 112 -> 104 on a sibling record), consistent with the repo's distance-inflation fieldnotes; the submitted claim is the deepest search's.

Near-misses from the same ideal family collapsed under deepening: several [[674,44,<=112]]-screen siblings fell to d <= 104-108, and the k = 126/168 cells at n = 254/674 collapsed to d <= 8 (rate too high for the blocklength).

Dead ends

  • m = 251, 257, 331 produced nothing: their cyclotomic-coset degrees

    • (50, 16, 30) do not divide the swept degree targets, so every degree grid was empty. The feasibility filter made this costless; the lesson is to scale the degree grid by e = ord_m(2) per m.

  • High-rate cells (k = 2m/4 and above at these m) give d <= 8 across the

    • board: the BCH run-length filter admits cofactors there, but the quantum distance collapses.

  • The q-ary constructions of arXiv:2609.22503 themselves: no binary entry

    • exists (Euclidean families need (r+delta-1) | (q-1); the Hermitian q = 2 corner gives only n = 3u or 5u codes with d <= 6), so only the zero-set design principle was portable.

Tools

Model: GLM 5.3 Flash (Zed agent). Harness: research/kit (css, surrogate, gf2_fast accelerator) plus a new constructor module implementing the GF(2^e) zero-set evaluation, the BCH feasibility filter, and the sweep driver; packaging and gating through ./qldpc submit (20k RIS + 1M accelerator trials, then the full local verifier). Compute: ~92 min sweep + per-code deep confirms, on a machine shared with two concurrent campaigns (timings inflated).

Reproduction

Build the circulants over Z_127: A = circ(a), B = circ(b) with first rows a = [8, 29, 33, 37, 61, 76, 98, 109] and b = [1, 7, 42, 61, 85, 114, 124, 125] (0/1 vectors of length 127, ones at the listed indices), then H_X = [A | B] and H_Z = [B^T | A^T]. The common divisor is g_int = 54066391421 (little-endian coefficient bitmask of g(x) | x^127 - 1), of degree 35; its zero set has longest consecutive run 3 and its complement 8, so the BCH floor on any cofactor is 4 and the pure-logical floor through ker(B) is 9. The cofactors above are multiples of g mod x^127 - 1; k = 2 deg(g) = 72. The sweep method (GF(2^e) zero-set evaluation, BCH feasibility filter, Prange inside the ideal) is described in full above; the parameters in this section rebuild (H_X, H_Z) directly.

Parity checks

X-checks 127 (max weight 16) · Z-checks 127 (max weight 16)
H_X (127 checks, sparse supports)
[8, 29, 33, 37, 61, 76, 98, 109, 128, 134, 169, 188, 212, 241, 251, 252] [9, 30, 34, 38, 62, 77, 99, 110, 129, 135, 170, 189, 213, 242, 252, 253] [10, 31, 35, 39, 63, 78, 100, 111, 127, 130, 136, 171, 190, 214, 243, 253] [11, 32, 36, 40, 64, 79, 101, 112, 127, 128, 131, 137, 172, 191, 215, 244] [12, 33, 37, 41, 65, 80, 102, 113, 128, 129, 132, 138, 173, 192, 216, 245] [13, 34, 38, 42, 66, 81, 103, 114, 129, 130, 133, 139, 174, 193, 217, 246] [14, 35, 39, 43, 67, 82, 104, 115, 130, 131, 134, 140, 175, 194, 218, 247] [15, 36, 40, 44, 68, 83, 105, 116, 131, 132, 135, 141, 176, 195, 219, 248] [16, 37, 41, 45, 69, 84, 106, 117, 132, 133, 136, 142, 177, 196, 220, 249] [17, 38, 42, 46, 70, 85, 107, 118, 133, 134, 137, 143, 178, 197, 221, 250] [18, 39, 43, 47, 71, 86, 108, 119, 134, 135, 138, 144, 179, 198, 222, 251] [19, 40, 44, 48, 72, 87, 109, 120, 135, 136, 139, 145, 180, 199, 223, 252] [20, 41, 45, 49, 73, 88, 110, 121, 136, 137, 140, 146, 181, 200, 224, 253] [21, 42, 46, 50, 74, 89, 111, 122, 127, 137, 138, 141, 147, 182, 201, 225] [22, 43, 47, 51, 75, 90, 112, 123, 128, 138, 139, 142, 148, 183, 202, 226] [23, 44, 48, 52, 76, 91, 113, 124, 129, 139, 140, 143, 149, 184, 203, 227] [24, 45, 49, 53, 77, 92, 114, 125, 130, 140, 141, 144, 150, 185, 204, 228] [25, 46, 50, 54, 78, 93, 115, 126, 131, 141, 142, 145, 151, 186, 205, 229] [0, 26, 47, 51, 55, 79, 94, 116, 132, 142, 143, 146, 152, 187, 206, 230] [1, 27, 48, 52, 56, 80, 95, 117, 133, 143, 144, 147, 153, 188, 207, 231] [2, 28, 49, 53, 57, 81, 96, 118, 134, 144, 145, 148, 154, 189, 208, 232] [3, 29, 50, 54, 58, 82, 97, 119, 135, 145, 146, 149, 155, 190, 209, 233] [4, 30, 51, 55, 59, 83, 98, 120, 136, 146, 147, 150, 156, 191, 210, 234] [5, 31, 52, 56, 60, 84, 99, 121, 137, 147, 148, 151, 157, 192, 211, 235] [6, 32, 53, 57, 61, 85, 100, 122, 138, 148, 149, 152, 158, 193, 212, 236] [7, 33, 54, 58, 62, 86, 101, 123, 139, 149, 150, 153, 159, 194, 213, 237] [8, 34, 55, 59, 63, 87, 102, 124, 140, 150, 151, 154, 160, 195, 214, 238] [9, 35, 56, 60, 64, 88, 103, 125, 141, 151, 152, 155, 161, 196, 215, 239] [10, 36, 57, 61, 65, 89, 104, 126, 142, 152, 153, 156, 162, 197, 216, 240] [0, 11, 37, 58, 62, 66, 90, 105, 143, 153, 154, 157, 163, 198, 217, 241] [1, 12, 38, 59, 63, 67, 91, 106, 144, 154, 155, 158, 164, 199, 218, 242] [2, 13, 39, 60, 64, 68, 92, 107, 145, 155, 156, 159, 165, 200, 219, 243] [3, 14, 40, 61, 65, 69, 93, 108, 146, 156, 157, 160, 166, 201, 220, 244] [4, 15, 41, 62, 66, 70, 94, 109, 147, 157, 158, 161, 167, 202, 221, 245] [5, 16, 42, 63, 67, 71, 95, 110, 148, 158, 159, 162, 168, 203, 222, 246] [6, 17, 43, 64, 68, 72, 96, 111, 149, 159, 160, 163, 169, 204, 223, 247] [7, 18, 44, 65, 69, 73, 97, 112, 150, 160, 161, 164, 170, 205, 224, 248] [8, 19, 45, 66, 70, 74, 98, 113, 151, 161, 162, 165, 171, 206, 225, 249] [9, 20, 46, 67, 71, 75, 99, 114, 152, 162, 163, 166, 172, 207, 226, 250] [10, 21, 47, 68, 72, 76, 100, 115, 153, 163, 164, 167, 173, 208, 227, 251] [11, 22, 48, 69, 73, 77, 101, 116, 154, 164, 165, 168, 174, 209, 228, 252] [12, 23, 49, 70, 74, 78, 102, 117, 155, 165, 166, 169, 175, 210, 229, 253] [13, 24, 50, 71, 75, 79, 103, 118, 127, 156, 166, 167, 170, 176, 211, 230] [14, 25, 51, 72, 76, 80, 104, 119, 128, 157, 167, 168, 171, 177, 212, 231] [15, 26, 52, 73, 77, 81, 105, 120, 129, 158, 168, 169, 172, 178, 213, 232] [16, 27, 53, 74, 78, 82, 106, 121, 130, 159, 169, 170, 173, 179, 214, 233] [17, 28, 54, 75, 79, 83, 107, 122, 131, 160, 170, 171, 174, 180, 215, 234] [18, 29, 55, 76, 80, 84, 108, 123, 132, 161, 171, 172, 175, 181, 216, 235] [19, 30, 56, 77, 81, 85, 109, 124, 133, 162, 172, 173, 176, 182, 217, 236] [20, 31, 57, 78, 82, 86, 110, 125, 134, 163, 173, 174, 177, 183, 218, 237] [21, 32, 58, 79, 83, 87, 111, 126, 135, 164, 174, 175, 178, 184, 219, 238] [0, 22, 33, 59, 80, 84, 88, 112, 136, 165, 175, 176, 179, 185, 220, 239] [1, 23, 34, 60, 81, 85, 89, 113, 137, 166, 176, 177, 180, 186, 221, 240] [2, 24, 35, 61, 82, 86, 90, 114, 138, 167, 177, 178, 181, 187, 222, 241] [3, 25, 36, 62, 83, 87, 91, 115, 139, 168, 178, 179, 182, 188, 223, 242] [4, 26, 37, 63, 84, 88, 92, 116, 140, 169, 179, 180, 183, 189, 224, 243] [5, 27, 38, 64, 85, 89, 93, 117, 141, 170, 180, 181, 184, 190, 225, 244] [6, 28, 39, 65, 86, 90, 94, 118, 142, 171, 181, 182, 185, 191, 226, 245] [7, 29, 40, 66, 87, 91, 95, 119, 143, 172, 182, 183, 186, 192, 227, 246] [8, 30, 41, 67, 88, 92, 96, 120, 144, 173, 183, 184, 187, 193, 228, 247] [9, 31, 42, 68, 89, 93, 97, 121, 145, 174, 184, 185, 188, 194, 229, 248] [10, 32, 43, 69, 90, 94, 98, 122, 146, 175, 185, 186, 189, 195, 230, 249] [11, 33, 44, 70, 91, 95, 99, 123, 147, 176, 186, 187, 190, 196, 231, 250] [12, 34, 45, 71, 92, 96, 100, 124, 148, 177, 187, 188, 191, 197, 232, 251] [13, 35, 46, 72, 93, 97, 101, 125, 149, 178, 188, 189, 192, 198, 233, 252] [14, 36, 47, 73, 94, 98, 102, 126, 150, 179, 189, 190, 193, 199, 234, 253] [0, 15, 37, 48, 74, 95, 99, 103, 127, 151, 180, 190, 191, 194, 200, 235] [1, 16, 38, 49, 75, 96, 100, 104, 128, 152, 181, 191, 192, 195, 201, 236] [2, 17, 39, 50, 76, 97, 101, 105, 129, 153, 182, 192, 193, 196, 202, 237] [3, 18, 40, 51, 77, 98, 102, 106, 130, 154, 183, 193, 194, 197, 203, 238] [4, 19, 41, 52, 78, 99, 103, 107, 131, 155, 184, 194, 195, 198, 204, 239] [5, 20, 42, 53, 79, 100, 104, 108, 132, 156, 185, 195, 196, 199, 205, 240] [6, 21, 43, 54, 80, 101, 105, 109, 133, 157, 186, 196, 197, 200, 206, 241] [7, 22, 44, 55, 81, 102, 106, 110, 134, 158, 187, 197, 198, 201, 207, 242] [8, 23, 45, 56, 82, 103, 107, 111, 135, 159, 188, 198, 199, 202, 208, 243] [9, 24, 46, 57, 83, 104, 108, 112, 136, 160, 189, 199, 200, 203, 209, 244] [10, 25, 47, 58, 84, 105, 109, 113, 137, 161, 190, 200, 201, 204, 210, 245] [11, 26, 48, 59, 85, 106, 110, 114, 138, 162, 191, 201, 202, 205, 211, 246] [12, 27, 49, 60, 86, 107, 111, 115, 139, 163, 192, 202, 203, 206, 212, 247] [13, 28, 50, 61, 87, 108, 112, 116, 140, 164, 193, 203, 204, 207, 213, 248] [14, 29, 51, 62, 88, 109, 113, 117, 141, 165, 194, 204, 205, 208, 214, 249] [15, 30, 52, 63, 89, 110, 114, 118, 142, 166, 195, 205, 206, 209, 215, 250] [16, 31, 53, 64, 90, 111, 115, 119, 143, 167, 196, 206, 207, 210, 216, 251] [17, 32, 54, 65, 91, 112, 116, 120, 144, 168, 197, 207, 208, 211, 217, 252] [18, 33, 55, 66, 92, 113, 117, 121, 145, 169, 198, 208, 209, 212, 218, 253] [19, 34, 56, 67, 93, 114, 118, 122, 127, 146, 170, 199, 209, 210, 213, 219] [20, 35, 57, 68, 94, 115, 119, 123, 128, 147, 171, 200, 210, 211, 214, 220] [21, 36, 58, 69, 95, 116, 120, 124, 129, 148, 172, 201, 211, 212, 215, 221] [22, 37, 59, 70, 96, 117, 121, 125, 130, 149, 173, 202, 212, 213, 216, 222] [23, 38, 60, 71, 97, 118, 122, 126, 131, 150, 174, 203, 213, 214, 217, 223] [0, 24, 39, 61, 72, 98, 119, 123, 132, 151, 175, 204, 214, 215, 218, 224] [1, 25, 40, 62, 73, 99, 120, 124, 133, 152, 176, 205, 215, 216, 219, 225] [2, 26, 41, 63, 74, 100, 121, 125, 134, 153, 177, 206, 216, 217, 220, 226] [3, 27, 42, 64, 75, 101, 122, 126, 135, 154, 178, 207, 217, 218, 221, 227] [0, 4, 28, 43, 65, 76, 102, 123, 136, 155, 179, 208, 218, 219, 222, 228] [1, 5, 29, 44, 66, 77, 103, 124, 137, 156, 180, 209, 219, 220, 223, 229] [2, 6, 30, 45, 67, 78, 104, 125, 138, 157, 181, 210, 220, 221, 224, 230] [3, 7, 31, 46, 68, 79, 105, 126, 139, 158, 182, 211, 221, 222, 225, 231] [0, 4, 8, 32, 47, 69, 80, 106, 140, 159, 183, 212, 222, 223, 226, 232] [1, 5, 9, 33, 48, 70, 81, 107, 141, 160, 184, 213, 223, 224, 227, 233] [2, 6, 10, 34, 49, 71, 82, 108, 142, 161, 185, 214, 224, 225, 228, 234] [3, 7, 11, 35, 50, 72, 83, 109, 143, 162, 186, 215, 225, 226, 229, 235] [4, 8, 12, 36, 51, 73, 84, 110, 144, 163, 187, 216, 226, 227, 230, 236] [5, 9, 13, 37, 52, 74, 85, 111, 145, 164, 188, 217, 227, 228, 231, 237] [6, 10, 14, 38, 53, 75, 86, 112, 146, 165, 189, 218, 228, 229, 232, 238] [7, 11, 15, 39, 54, 76, 87, 113, 147, 166, 190, 219, 229, 230, 233, 239] [8, 12, 16, 40, 55, 77, 88, 114, 148, 167, 191, 220, 230, 231, 234, 240] [9, 13, 17, 41, 56, 78, 89, 115, 149, 168, 192, 221, 231, 232, 235, 241] [10, 14, 18, 42, 57, 79, 90, 116, 150, 169, 193, 222, 232, 233, 236, 242] [11, 15, 19, 43, 58, 80, 91, 117, 151, 170, 194, 223, 233, 234, 237, 243] [12, 16, 20, 44, 59, 81, 92, 118, 152, 171, 195, 224, 234, 235, 238, 244] [13, 17, 21, 45, 60, 82, 93, 119, 153, 172, 196, 225, 235, 236, 239, 245] [14, 18, 22, 46, 61, 83, 94, 120, 154, 173, 197, 226, 236, 237, 240, 246] [15, 19, 23, 47, 62, 84, 95, 121, 155, 174, 198, 227, 237, 238, 241, 247] [16, 20, 24, 48, 63, 85, 96, 122, 156, 175, 199, 228, 238, 239, 242, 248] [17, 21, 25, 49, 64, 86, 97, 123, 157, 176, 200, 229, 239, 240, 243, 249] [18, 22, 26, 50, 65, 87, 98, 124, 158, 177, 201, 230, 240, 241, 244, 250] [19, 23, 27, 51, 66, 88, 99, 125, 159, 178, 202, 231, 241, 242, 245, 251] [20, 24, 28, 52, 67, 89, 100, 126, 160, 179, 203, 232, 242, 243, 246, 252] [0, 21, 25, 29, 53, 68, 90, 101, 161, 180, 204, 233, 243, 244, 247, 253] [1, 22, 26, 30, 54, 69, 91, 102, 127, 162, 181, 205, 234, 244, 245, 248] [2, 23, 27, 31, 55, 70, 92, 103, 128, 163, 182, 206, 235, 245, 246, 249] [3, 24, 28, 32, 56, 71, 93, 104, 129, 164, 183, 207, 236, 246, 247, 250] [4, 25, 29, 33, 57, 72, 94, 105, 130, 165, 184, 208, 237, 247, 248, 251] [5, 26, 30, 34, 58, 73, 95, 106, 131, 166, 185, 209, 238, 248, 249, 252] [6, 27, 31, 35, 59, 74, 96, 107, 132, 167, 186, 210, 239, 249, 250, 253] [7, 28, 32, 36, 60, 75, 97, 108, 127, 133, 168, 187, 211, 240, 250, 251]
H_Z (127 checks, sparse supports)
[2, 3, 13, 42, 66, 85, 120, 126, 145, 156, 178, 193, 217, 221, 225, 246] [0, 3, 4, 14, 43, 67, 86, 121, 146, 157, 179, 194, 218, 222, 226, 247] [1, 4, 5, 15, 44, 68, 87, 122, 147, 158, 180, 195, 219, 223, 227, 248] [2, 5, 6, 16, 45, 69, 88, 123, 148, 159, 181, 196, 220, 224, 228, 249] [3, 6, 7, 17, 46, 70, 89, 124, 149, 160, 182, 197, 221, 225, 229, 250] [4, 7, 8, 18, 47, 71, 90, 125, 150, 161, 183, 198, 222, 226, 230, 251] [5, 8, 9, 19, 48, 72, 91, 126, 151, 162, 184, 199, 223, 227, 231, 252] [0, 6, 9, 10, 20, 49, 73, 92, 152, 163, 185, 200, 224, 228, 232, 253] [1, 7, 10, 11, 21, 50, 74, 93, 127, 153, 164, 186, 201, 225, 229, 233] [2, 8, 11, 12, 22, 51, 75, 94, 128, 154, 165, 187, 202, 226, 230, 234] [3, 9, 12, 13, 23, 52, 76, 95, 129, 155, 166, 188, 203, 227, 231, 235] [4, 10, 13, 14, 24, 53, 77, 96, 130, 156, 167, 189, 204, 228, 232, 236] [5, 11, 14, 15, 25, 54, 78, 97, 131, 157, 168, 190, 205, 229, 233, 237] [6, 12, 15, 16, 26, 55, 79, 98, 132, 158, 169, 191, 206, 230, 234, 238] [7, 13, 16, 17, 27, 56, 80, 99, 133, 159, 170, 192, 207, 231, 235, 239] [8, 14, 17, 18, 28, 57, 81, 100, 134, 160, 171, 193, 208, 232, 236, 240] [9, 15, 18, 19, 29, 58, 82, 101, 135, 161, 172, 194, 209, 233, 237, 241] [10, 16, 19, 20, 30, 59, 83, 102, 136, 162, 173, 195, 210, 234, 238, 242] [11, 17, 20, 21, 31, 60, 84, 103, 137, 163, 174, 196, 211, 235, 239, 243] [12, 18, 21, 22, 32, 61, 85, 104, 138, 164, 175, 197, 212, 236, 240, 244] [13, 19, 22, 23, 33, 62, 86, 105, 139, 165, 176, 198, 213, 237, 241, 245] [14, 20, 23, 24, 34, 63, 87, 106, 140, 166, 177, 199, 214, 238, 242, 246] [15, 21, 24, 25, 35, 64, 88, 107, 141, 167, 178, 200, 215, 239, 243, 247] [16, 22, 25, 26, 36, 65, 89, 108, 142, 168, 179, 201, 216, 240, 244, 248] [17, 23, 26, 27, 37, 66, 90, 109, 143, 169, 180, 202, 217, 241, 245, 249] [18, 24, 27, 28, 38, 67, 91, 110, 144, 170, 181, 203, 218, 242, 246, 250] [19, 25, 28, 29, 39, 68, 92, 111, 145, 171, 182, 204, 219, 243, 247, 251] [20, 26, 29, 30, 40, 69, 93, 112, 146, 172, 183, 205, 220, 244, 248, 252] [21, 27, 30, 31, 41, 70, 94, 113, 147, 173, 184, 206, 221, 245, 249, 253] [22, 28, 31, 32, 42, 71, 95, 114, 127, 148, 174, 185, 207, 222, 246, 250] [23, 29, 32, 33, 43, 72, 96, 115, 128, 149, 175, 186, 208, 223, 247, 251] [24, 30, 33, 34, 44, 73, 97, 116, 129, 150, 176, 187, 209, 224, 248, 252] [25, 31, 34, 35, 45, 74, 98, 117, 130, 151, 177, 188, 210, 225, 249, 253] [26, 32, 35, 36, 46, 75, 99, 118, 127, 131, 152, 178, 189, 211, 226, 250] [27, 33, 36, 37, 47, 76, 100, 119, 128, 132, 153, 179, 190, 212, 227, 251] [28, 34, 37, 38, 48, 77, 101, 120, 129, 133, 154, 180, 191, 213, 228, 252] [29, 35, 38, 39, 49, 78, 102, 121, 130, 134, 155, 181, 192, 214, 229, 253] [30, 36, 39, 40, 50, 79, 103, 122, 127, 131, 135, 156, 182, 193, 215, 230] [31, 37, 40, 41, 51, 80, 104, 123, 128, 132, 136, 157, 183, 194, 216, 231] [32, 38, 41, 42, 52, 81, 105, 124, 129, 133, 137, 158, 184, 195, 217, 232] [33, 39, 42, 43, 53, 82, 106, 125, 130, 134, 138, 159, 185, 196, 218, 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Code ID 254-72-17 · download JSON · raw on GitHub