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[[480,16,26]] d =
n
480
k
16
d
26
kd²/n
22.5333
w
6
X/Z
1

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Distance

X/Z asymmetry 1 · d_X = 26, d_Z = 26 · w_X = 6, w_Z = 6 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 26 · witness weight 26 (claimed exact)
witness operator (support, 26 qubits)
[7, 22, 24, 27, 70, 112, 126, 149, 193, 194, 223, 236, 239, 240, 266, 282, 299, 303, 330, 355, 366, 416, 432, 452, 463, 478]
d_Z 26 · witness weight 26 (claimed exact)
witness operator (support, 26 qubits)
[16, 39, 54, 61, 105, 151, 177, 195, 201, 208, 232, 237, 245, 259, 283, 293, 336, 374, 384, 385, 416, 423, 429, 441, 451, 475]
certificate exact, d = 26 · tropidist b03ec2d4077f (arXiv:2611.08247) exhaustive search · level solver: a solver verdict, no artifact a third party can check without re-running the encoding
X: no logical < 26 exists; Z: no logical < 26 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 8 · H_Z 8 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 6 · H_Z 6
qubit degrees H_X 3 · H_Z 3
trapping sets H_X (1,3)×480 (2,4)×3600 (3,5)×36000 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,3): 480 (2,4): 3600 (3,5): 36000 (3,7): 4800
trapping sets H_Z (1,3)×480 (2,4)×3600 (3,5)×36000 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,3): 480 (2,4): 3600 (3,5): 36000 (3,7): 4800

Construction & provenance

authors @TimoKellerMath
provenance submitted through the challenge
novelty new parameter set claimed by submitter
construction Two-block group algebra (2BGA) code C(G;a,b) over G = C12 x Dic5 = <z> x <x, y | x5, y4, y x y-1 = x-1>, |z| = 12, SmallGroup(240,40). Element z^c x^i y^j (c mod 12, i mod 5, j mod 4) has index 20c + 4i + j; it is qubit 20c + 4i + j of block 1 and 240 + 20c + 4i + j of block 2 (the indexing of 720-16-36 and 960-24-38); product (c,i,j)(c',i',j') = (c + c', i + (-1)^j i', j + j'). H_X = [L(a) | R(b)], H_Z = [R(b)^T | L(a)^T] with L(a)[g,h] = 1 iff g = alpha h, R(b)[g,h] = 1 iff g = h beta: the X-check at c is {s-1 c : s in a} in block 1 and {c t-1 : t in b} in block 2, the Z-check at c is {c t : t in b} and {s c : s in a}, checks in the order of the index of c. a = 1 + z8 x3 y2 + z11 y3, b = 1 + z2 x y2 + y. n = 480, k = 16, check weight 6 = 3 + 3, every qubit in 3 X-checks and 3 Z-checks. Found by a design from the representation theory of F_2[G]: all 16 logical qubits lie in one block M_2(F_4[C4 x C2]) of F_2[G], where the norms of a and b meet in a curvilinear point of length 4.
model Claude Claude Opus 5.5 (claimed, not verified)
builds on arXiv:2306.16400, arXiv:2305.06890, arXiv:2610.13880, arXiv:1611.07164, arXiv:2611.08247
date 2026-11-10
notes Exact distance: d_X = d_Z = 26. Every column of H_X and H_Z has weight 3, so every logical has even weight; two independently written exhaustive searches (exactA, exactB), anchored at the orbits of a Tanner-graph automorphism group of order 240, find no nontrivial logical of weight <= 24 on either side, in two sets of runs on two instances with independently computed groups; see the research note and certs/480-16-26.json (programs, completeness proofs, instances and logs: github.com/TimoKellerMath/quantum-error-correction @ aaa18674c9a1, two-block-and-amplified-codes/). tropidist b03ec2d4077f reached only d_X, d_Z >= 22 in 1200 s per side. Novelty: no [[480,16]] entry on the board (commit 8042f9da) and no published code with these parameters known to us (literature checked: see the note). The census of weight-6 2BGA codes over C_m x Dic5 reported in notes/720-16-36.md (group orders up to 480) very likely contains this code; it is not submitted or described there. No entry has these n and k; checked, not equivalent to an existing entry.
family 2BGA coset (a tag, not a ranking)
locality unrestricted (computed from the layout)
weight class weight ≤ 6 (computed)

How this code was found

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

[[480,16,26]]: weight-6 two-block group algebra code over C12 x Dic5

Direction & hypothesis

Cell: check weight at most 6, unrestricted locality (no layout submitted). The leaders of this cell are two-block group algebra (2BGA) codes over non-abelian groups with a large centre, among them 960-24-38 and 720-16-36 over C_m x Dic5. Hypothesis: k of C(G;a,b) can be read off from the blocks of F_2[G], and choosing a and b so that k is carried by a single block, in which the two norms meet in a curvilinear point, gives connected codes with large distance. For G = C_m x Dic5 with m = 3 x 2^e the subgroup A = <z, x, y^2> is abelian of index 2, its 2-part A_2 is central, and its odd part <t> is cyclic of order 15 (t = z^4 x for m = 12). A Galois orbit of characters of order 15 of <t> has the block M_2(F_4[A_2]); there a and b act by 2 x 2 Clifford symbols over the local ring O = F_4[A_2], and if both residues have rank at least 1 the orbit contributes 4 dim O/(N(a), N(b)) to k, where N(a), N(b) are the determinants (norms in F_2[A]).

What was searched

Normal forms a = 1 + u + y v, b = 1 + u' + v' y with u, v, u', v' in A (every weight-3 element with two terms in one coset of A has this form up to two-sided translations, which give equivalent codes). At an order-15 character the residue of N(a) vanishes for exactly one value of the C3-part of v per value of the odd part of u != 1, so the pairs that carry k at a given orbit can be listed exactly. We enumerated all normal-form pairs on C_m x D5 and C_m x Dic5, m = 6, 12, 24, by the ideal (N(a), N(b)) at each orbit. On C12 x Dic5 the class with contact length 4 at one fixed order-15 orbit and nothing elsewhere has 78848 pairs (as many again for the other orbit), all with k = 16. We drew 320 of them uniformly and screened each (upper bounds only) by an information-set search with 1e3 trials per side plus searches restricted to words invariant under central subgroups; for comparison 80 uniform weight-3 pairs with k = 16 on the same group and 60 pairs carried by the order-3 characters. In all, 1420 screened codes on six groups, 47 CPU-minutes.

Related work: the board contributor @MicheldeMessieres reports publicly, in notes/720-16-36.md, an exhaustive census, up to equivalence, of the weight-6 (3+3) 2BGA codes over C_m x H for H among small non-abelian groups including Dic5, for group orders up to 480, in the same convention and indexing; only its list of codes is not published. C12 x Dic5 has order 240, so that census very likely contains this code; it was not submitted or described there. We found the code independently, by the design above (a single carrying orbit of order 15, the curvilinear point Spec F_4[eps]/(eps^4)); our contribution is its identification and the exact distance.

Evidence trail

  • Screening: 10 of the 320 designed pairs reached 26 or more (one of them 28, lowered to 26 by a deeper search), and all ten are this code (canonical forms of the Tanner graphs); the best uniform pair with k = 16 reached 20, the best order-3 pair 16.
  • Construction: provenance.construction; rank H_X = rank H_Z = 232, k = 16, every column of weight 3, Tanner graph connected; rebuilt independently with a Python group law and with Magma from the presentation (SmallGroup(240,40)).
  • Representation theory (computed, Propositions 3 to 5 of the README of the package below): all 16 logical qubits lie in the block of the factor t^4 + t + 1 of t^15 + 1; there the residues of both Clifford symbols have rank 1 and O/(N(a), N(b)) has length 4 and Hilbert function (1,1,1,1), so it is F_4[eps]/(eps^4) over the residue field, and k = 2 x 2 x 4. The Brauer sandwich gives k_ss/k/k_C = 4/16/32: two simple modules of dimension 2 with kappa(a) = kappa(b) = 1 and Cartan entries 8 = |A_2|; the semisimple part carries 4 logical qubits and the central defect group the other 12. Along the 2-tower, the same supports over C_m x Dic5 give k = 4, 8, 16, 16 for m = 3, 6, 12, 24.
  • Upper bound: an information-set search with 2e4 trials per side found words of weight 26 on both sides (31 and 16 distinct ones) and nothing lighter; the entry carries one per side.
  • Lower bound: all rows of H_X sum to the all-one vector, and so do those of H_Z, so every logical has even weight and it suffices to exclude weight <= 24. Two independently written exhaustive programs (exactA, exactB), anchored at the orbits of the Tanner-graph automorphism group (order 240, two qubit orbits), find no nontrivial logical of weight <= 24 on either side, in two sets of runs on two instances whose groups were computed independently (nauty, Magma); nodes and CPU seconds for the sides Z / X:
  • first set (W = 25, searched 24), one anchor per orbit, earlier orbits excluded: exactA 1.06e8 / 1.05e8, 314 / 366 s; exactB 1.10e8 / 1.09e8, 349 / 402 s
  • second set (W = 24) on a relabelled instance: exactA with pattern classes of the single check orbit, 3.00e7 / 2.82e7, 50 / 47 s; exactB with the orbits in the other order, 1.22e8 / 1.19e8, 269 / 261 s
  • tropidist b03ec2d4077f (the board's encoding, 16 threads per side, on a qubit relabelling of this entry) certified d_X = d_Z = 26 exactly, in 5185 s and 5474 s wall time, with a returned vector of weight 26 on each side; an earlier single-threaded attempt (1200 s per side) had reached only d >= 22. Records, inputs, the permutation and a checker that it maps the rows of H_X and H_Z of this entry onto the inputs: github.com/TimoKellerMath/quantum-error-correction @ 77f905b6e8dd, two-block-and-amplified-codes/logs/trop480/.
  • Final claim: d_X = d_Z = 26 exactly, by three independent programs (exactA and exactB: Theorem 2 of the README, completeness proofs of both programs in their notes there; tropidist). certs/480-16-26.json is the tropidist certificate.

Dead ends

  • At equal k the design is not markedly better than uniform sampling: on C24 x Dic5 (n = 960, k = 24) 15 of 60 designed and 10 of 30 uniform pairs reached kd^2/n >= 24 in screening, all of them the board's 960-24-38 or one dominated second code. For pairs with two terms in one coset of A, k >= 16 already forces a single carrying orbit, so uniform pairs at equal k mostly are designed pairs. The design saves rank computations (a factor of about 70 at k = 16), not distance.
  • Contact schemes that are not curvilinear (Hilbert function (1,2,1)) gave at most 12 at n = 480 (18 codes); contact length 8 (k = 32) at most 12 at n = 480 and 20 at n = 960; carrying k at both order-15 orbits forces a and b into a subgroup of index 5, hence disconnected codes; the cyclic 2-part of C24 x D5 (n = 480, k = 16) gave at most 20 in 160 codes.
  • A double cover over C24 x Dic5 found in the screening (n = 960, k = 16): the lightest words found are the pulled-back words of weight 52; its distance is open.
  • Larger residue fields by uniform sampling: on C12 x Dic7 (n = 672) the connected codes with k = 16 reached at most 14, on C4 x Dic15 (n = 480) at most 12, and on C20 x Dic5 (n = 800) only 0.6 % of 5000 pairs had k > 0.
  • Literature checked without a [[480,16,d >= 26]] code or a code over C12 x Dic5: Lin and Pryadko (arXiv:2306.16400), G. Lee (arXiv:2610.13880), Aydin, Tamo and Barg (arXiv:2606.17268), Rajpurohit, Lalitha and Garani (arXiv:2610.12782), arXiv:2606.24808, arXiv:2608.08996, arXiv:2608.12509, the Error Correction Zoo; QECDB was not checked.

Tools

Claude Opus 5.5 (Claude Code); Python and Magma for the group algebra, the blocks, the census, the Brauer sandwich and the equivalence tests (with nauty); C for the screening and for the two exact programs, exactA and exactB, which generalize the two programs of weight6-exact-distances (github.com/TimoKellerMath/quantum-error-correction @ 2be467a7bd36) to any check weight and any group of qubit permutations, with completeness proofs in their notes; tropidist (Cheng, Guo, Pan, arXiv:2611.08247). About 2.7 CPU-hours in total: design, census and screening 1.4, exact searches 0.6, tropidist 0.7.

Reproduction

In two-block-and-amplified-codes/ of github.com/TimoKellerMath/quantum-error-correction @ aaa18674c9a1: python3 src/rebuild.py rebuilds H_X and H_Z from the group law and a, b, and checks k, the parity, the witnesses, both search instances with their groups, and the statements on the blocks; make long and make long-first rerun the exact searches and compare them with our logs. G = C12 x Dic5, z^c x^i y^j has index 20c + 4i + j (block 2: add 240), a = 1 + z^8 x^3 y^2 + z^11 y^3, b = 1 + z^2 x y^2 + y.

Parity checks

X-checks 240 (max weight 6) · Z-checks 240 (max weight 6)
H_X (240 checks, sparse supports)
[0, 21, 90, 240, 243, 458] [1, 22, 91, 240, 241, 447] [2, 23, 88, 241, 242, 456] [3, 20, 89, 242, 243, 445] [4, 37, 94, 244, 247, 442] [5, 38, 95, 244, 245, 451] [6, 39, 92, 245, 246, 440] [7, 36, 93, 246, 247, 449] [8, 33, 98, 248, 251, 446] [9, 34, 99, 248, 249, 455] [10, 35, 96, 249, 250, 444] [11, 32, 97, 250, 251, 453] [12, 29, 82, 252, 255, 450] [13, 30, 83, 252, 253, 459] [14, 31, 80, 253, 254, 448] [15, 28, 81, 254, 255, 457] [16, 25, 86, 256, 259, 454] [17, 26, 87, 256, 257, 443] [18, 27, 84, 257, 258, 452] [19, 24, 85, 258, 259, 441] [20, 41, 110, 260, 263, 478] [21, 42, 111, 260, 261, 467] [22, 43, 108, 261, 262, 476] [23, 40, 109, 262, 263, 465] [24, 57, 114, 264, 267, 462] [25, 58, 115, 264, 265, 471] [26, 59, 112, 265, 266, 460] [27, 56, 113, 266, 267, 469] [28, 53, 118, 268, 271, 466] [29, 54, 119, 268, 269, 475] [30, 55, 116, 269, 270, 464] [31, 52, 117, 270, 271, 473] [32, 49, 102, 272, 275, 470] [33, 50, 103, 272, 273, 479] [34, 51, 100, 273, 274, 468] [35, 48, 101, 274, 275, 477] [36, 45, 106, 276, 279, 474] [37, 46, 107, 276, 277, 463] [38, 47, 104, 277, 278, 472] [39, 44, 105, 278, 279, 461] [40, 61, 130, 258, 280, 283] [41, 62, 131, 247, 280, 281] [42, 63, 128, 256, 281, 282] [43, 60, 129, 245, 282, 283] [44, 77, 134, 242, 284, 287] [45, 78, 135, 251, 284, 285] [46, 79, 132, 240, 285, 286] [47, 76, 133, 249, 286, 287] [48, 73, 138, 246, 288, 291] [49, 74, 139, 255, 288, 289] [50, 75, 136, 244, 289, 290] [51, 72, 137, 253, 290, 291] [52, 69, 122, 250, 292, 295] [53, 70, 123, 259, 292, 293] [54, 71, 120, 248, 293, 294] [55, 68, 121, 257, 294, 295] [56, 65, 126, 254, 296, 299] [57, 66, 127, 243, 296, 297] [58, 67, 124, 252, 297, 298] [59, 64, 125, 241, 298, 299] [60, 81, 150, 278, 300, 303] [61, 82, 151, 267, 300, 301] [62, 83, 148, 276, 301, 302] [63, 80, 149, 265, 302, 303] [64, 97, 154, 262, 304, 307] [65, 98, 155, 271, 304, 305] [66, 99, 152, 260, 305, 306] [67, 96, 153, 269, 306, 307] [68, 93, 158, 266, 308, 311] [69, 94, 159, 275, 308, 309] [70, 95, 156, 264, 309, 310] [71, 92, 157, 273, 310, 311] [72, 89, 142, 270, 312, 315] [73, 90, 143, 279, 312, 313] [74, 91, 140, 268, 313, 314] [75, 88, 141, 277, 314, 315] [76, 85, 146, 274, 316, 319] [77, 86, 147, 263, 316, 317] [78, 87, 144, 272, 317, 318] [79, 84, 145, 261, 318, 319] [80, 101, 170, 298, 320, 323] [81, 102, 171, 287, 320, 321] [82, 103, 168, 296, 321, 322] [83, 100, 169, 285, 322, 323] [84, 117, 174, 282, 324, 327] [85, 118, 175, 291, 324, 325] [86, 119, 172, 280, 325, 326] [87, 116, 173, 289, 326, 327] [88, 113, 178, 286, 328, 331] [89, 114, 179, 295, 328, 329] [90, 115, 176, 284, 329, 330] [91, 112, 177, 293, 330, 331] [92, 109, 162, 290, 332, 335] [93, 110, 163, 299, 332, 333] [94, 111, 160, 288, 333, 334] [95, 108, 161, 297, 334, 335] [96, 105, 166, 294, 336, 339] [97, 106, 167, 283, 336, 337] [98, 107, 164, 292, 337, 338] [99, 104, 165, 281, 338, 339] [100, 121, 190, 318, 340, 343] [101, 122, 191, 307, 340, 341] [102, 123, 188, 316, 341, 342] [103, 120, 189, 305, 342, 343] [104, 137, 194, 302, 344, 347] [105, 138, 195, 311, 344, 345] [106, 139, 192, 300, 345, 346] [107, 136, 193, 309, 346, 347] [108, 133, 198, 306, 348, 351] [109, 134, 199, 315, 348, 349] [110, 135, 196, 304, 349, 350] [111, 132, 197, 313, 350, 351] [112, 129, 182, 310, 352, 355] [113, 130, 183, 319, 352, 353] [114, 131, 180, 308, 353, 354] [115, 128, 181, 317, 354, 355] [116, 125, 186, 314, 356, 359] [117, 126, 187, 303, 356, 357] [118, 127, 184, 312, 357, 358] [119, 124, 185, 301, 358, 359] [120, 141, 210, 338, 360, 363] [121, 142, 211, 327, 360, 361] [122, 143, 208, 336, 361, 362] [123, 140, 209, 325, 362, 363] [124, 157, 214, 322, 364, 367] [125, 158, 215, 331, 364, 365] [126, 159, 212, 320, 365, 366] [127, 156, 213, 329, 366, 367] [128, 153, 218, 326, 368, 371] [129, 154, 219, 335, 368, 369] [130, 155, 216, 324, 369, 370] [131, 152, 217, 333, 370, 371] [132, 149, 202, 330, 372, 375] [133, 150, 203, 339, 372, 373] [134, 151, 200, 328, 373, 374] [135, 148, 201, 337, 374, 375] [136, 145, 206, 334, 376, 379] [137, 146, 207, 323, 376, 377] [138, 147, 204, 332, 377, 378] [139, 144, 205, 321, 378, 379] [140, 161, 230, 358, 380, 383] [141, 162, 231, 347, 380, 381] [142, 163, 228, 356, 381, 382] [143, 160, 229, 345, 382, 383] [144, 177, 234, 342, 384, 387] [145, 178, 235, 351, 384, 385] [146, 179, 232, 340, 385, 386] [147, 176, 233, 349, 386, 387] [148, 173, 238, 346, 388, 391] [149, 174, 239, 355, 388, 389] [150, 175, 236, 344, 389, 390] [151, 172, 237, 353, 390, 391] [152, 169, 222, 350, 392, 395] [153, 170, 223, 359, 392, 393] [154, 171, 220, 348, 393, 394] [155, 168, 221, 357, 394, 395] [156, 165, 226, 354, 396, 399] [157, 166, 227, 343, 396, 397] [158, 167, 224, 352, 397, 398] [159, 164, 225, 341, 398, 399] [10, 160, 181, 378, 400, 403] [11, 161, 182, 367, 400, 401] [8, 162, 183, 376, 401, 402] [9, 163, 180, 365, 402, 403] [14, 164, 197, 362, 404, 407] [15, 165, 198, 371, 404, 405] [12, 166, 199, 360, 405, 406] [13, 167, 196, 369, 406, 407] [18, 168, 193, 366, 408, 411] [19, 169, 194, 375, 408, 409] [16, 170, 195, 364, 409, 410] [17, 171, 192, 373, 410, 411] [2, 172, 189, 370, 412, 415] [3, 173, 190, 379, 412, 413] [0, 174, 191, 368, 413, 414] [1, 175, 188, 377, 414, 415] [6, 176, 185, 374, 416, 419] [7, 177, 186, 363, 416, 417] [4, 178, 187, 372, 417, 418] [5, 179, 184, 361, 418, 419] [30, 180, 201, 398, 420, 423] [31, 181, 202, 387, 420, 421] [28, 182, 203, 396, 421, 422] [29, 183, 200, 385, 422, 423] [34, 184, 217, 382, 424, 427] [35, 185, 218, 391, 424, 425] [32, 186, 219, 380, 425, 426] [33, 187, 216, 389, 426, 427] [38, 188, 213, 386, 428, 431] [39, 189, 214, 395, 428, 429] [36, 190, 215, 384, 429, 430] [37, 191, 212, 393, 430, 431] [22, 192, 209, 390, 432, 435] [23, 193, 210, 399, 432, 433] [20, 194, 211, 388, 433, 434] [21, 195, 208, 397, 434, 435] [26, 196, 205, 394, 436, 439] [27, 197, 206, 383, 436, 437] [24, 198, 207, 392, 437, 438] [25, 199, 204, 381, 438, 439] [50, 200, 221, 418, 440, 443] [51, 201, 222, 407, 440, 441] [48, 202, 223, 416, 441, 442] [49, 203, 220, 405, 442, 443] [54, 204, 237, 402, 444, 447] [55, 205, 238, 411, 444, 445] [52, 206, 239, 400, 445, 446] [53, 207, 236, 409, 446, 447] [58, 208, 233, 406, 448, 451] [59, 209, 234, 415, 448, 449] [56, 210, 235, 404, 449, 450] [57, 211, 232, 413, 450, 451] [42, 212, 229, 410, 452, 455] [43, 213, 230, 419, 452, 453] [40, 214, 231, 408, 453, 454] [41, 215, 228, 417, 454, 455] [46, 216, 225, 414, 456, 459] [47, 217, 226, 403, 456, 457] [44, 218, 227, 412, 457, 458] [45, 219, 224, 401, 458, 459] [1, 70, 220, 438, 460, 463] [2, 71, 221, 427, 460, 461] [3, 68, 222, 436, 461, 462] [0, 69, 223, 425, 462, 463] [17, 74, 224, 422, 464, 467] [18, 75, 225, 431, 464, 465] [19, 72, 226, 420, 465, 466] [16, 73, 227, 429, 466, 467] [13, 78, 228, 426, 468, 471] [14, 79, 229, 435, 468, 469] [15, 76, 230, 424, 469, 470] [12, 77, 231, 433, 470, 471] [9, 62, 232, 430, 472, 475] [10, 63, 233, 439, 472, 473] [11, 60, 234, 428, 473, 474] [8, 61, 235, 437, 474, 475] [5, 66, 236, 434, 476, 479] [6, 67, 237, 423, 476, 477] [7, 64, 238, 432, 477, 478] [4, 65, 239, 421, 478, 479]
H_Z (240 checks, sparse supports)
[0, 1, 46, 240, 414, 463] [1, 2, 59, 241, 415, 460] [2, 3, 44, 242, 412, 461] [0, 3, 57, 243, 413, 462] [4, 5, 50, 244, 418, 479] [5, 6, 43, 245, 419, 476] [6, 7, 48, 246, 416, 477] [4, 7, 41, 247, 417, 478] [8, 9, 54, 248, 402, 475] [9, 10, 47, 249, 403, 472] [10, 11, 52, 250, 400, 473] [8, 11, 45, 251, 401, 474] [12, 13, 58, 252, 406, 471] [13, 14, 51, 253, 407, 468] [14, 15, 56, 254, 404, 469] [12, 15, 49, 255, 405, 470] [16, 17, 42, 256, 410, 467] [17, 18, 55, 257, 411, 464] [18, 19, 40, 258, 408, 465] [16, 19, 53, 259, 409, 466] [20, 21, 66, 243, 260, 434] [21, 22, 79, 240, 261, 435] [22, 23, 64, 241, 262, 432] [20, 23, 77, 242, 263, 433] [24, 25, 70, 259, 264, 438] [25, 26, 63, 256, 265, 439] [26, 27, 68, 257, 266, 436] [24, 27, 61, 258, 267, 437] [28, 29, 74, 255, 268, 422] [29, 30, 67, 252, 269, 423] [30, 31, 72, 253, 270, 420] [28, 31, 65, 254, 271, 421] [32, 33, 78, 251, 272, 426] [33, 34, 71, 248, 273, 427] [34, 35, 76, 249, 274, 424] [32, 35, 69, 250, 275, 425] [36, 37, 62, 247, 276, 430] [37, 38, 75, 244, 277, 431] [38, 39, 60, 245, 278, 428] [36, 39, 73, 246, 279, 429] [40, 41, 86, 263, 280, 454] [41, 42, 99, 260, 281, 455] [42, 43, 84, 261, 282, 452] [40, 43, 97, 262, 283, 453] [44, 45, 90, 279, 284, 458] [45, 46, 83, 276, 285, 459] [46, 47, 88, 277, 286, 456] [44, 47, 81, 278, 287, 457] [48, 49, 94, 275, 288, 442] [49, 50, 87, 272, 289, 443] [50, 51, 92, 273, 290, 440] [48, 51, 85, 274, 291, 441] [52, 53, 98, 271, 292, 446] [53, 54, 91, 268, 293, 447] [54, 55, 96, 269, 294, 444] [52, 55, 89, 270, 295, 445] [56, 57, 82, 267, 296, 450] [57, 58, 95, 264, 297, 451] [58, 59, 80, 265, 298, 448] [56, 59, 93, 266, 299, 449] [60, 61, 106, 283, 300, 474] [61, 62, 119, 280, 301, 475] [62, 63, 104, 281, 302, 472] [60, 63, 117, 282, 303, 473] [64, 65, 110, 299, 304, 478] [65, 66, 103, 296, 305, 479] [66, 67, 108, 297, 306, 476] [64, 67, 101, 298, 307, 477] [68, 69, 114, 295, 308, 462] [69, 70, 107, 292, 309, 463] [70, 71, 112, 293, 310, 460] [68, 71, 105, 294, 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475] [22, 236, 237, 390, 447, 476] [35, 237, 238, 391, 444, 477] [20, 238, 239, 388, 445, 478] [33, 236, 239, 389, 446, 479]
Code ID 480-16-26 · download JSON · raw on GitHub