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[[936,470,6]] d =
n
936
k
470
d
6
kd²/n
18.0769
w
8
X/Z
1

Share this result

Distance

X/Z asymmetry 1 · d_X = 6, d_Z = 6 · w_X = 8, w_Z = 8 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 6 · witness weight 6 (claimed exact)
witness operator (support, 6 qubits)
[0, 1, 3, 10, 27, 86]
d_Z 6 · witness weight 6 (claimed exact)
witness operator (support, 6 qubits)
[0, 1, 4, 7, 11, 151]
certificate exact, d = 6 · 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 < 6 exists; Z: no logical < 6 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 12 · H_Z 12 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 8 · H_Z 8
qubit degrees H_X 2 · H_Z 2
trapping sets H_X (1,2)×936 (2,2)×6552 (3,2)×45864 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,2): 936 (2,2): 6552 (3,2): 45864 (3,4): 13104
trapping sets H_Z (1,2)×936 (2,2)×6552 (3,2)×45864 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,2): 936 (2,2): 6552 (3,2): 45864 (3,4): 13104

Construction & provenance

authors @TimoKellerMath
provenance submitted through the challenge
novelty new parameter set claimed by submitter
construction Surface code of the orientably-regular map C235.23 of type {8,8} (genus 235) in M. Conder's list of chiral maps of genus 2 to 301, in its mirror image (Conder's relators hold for (r-1, s-1); mirror images give the same code). Rotation group G = <r,s | r8, s8, (r*s)2, s*r*s-2*r-3*s-2*r*s*r-1, s-1*r-1*s*r-1*s*r-2*s-1*r*s-1*r*s-1> of order 1872. Darts = elements of G (right multiplication), faces = cosets g<r>, vertices = cosets g<s>, edges = cosets g<rs> = {g, grs}. Qubits on the 936 edges, X-checks on the 234 vertices (weight 8), Z-checks on the 234 faces (weight 8), incidences mod 2: H_X and H_Z are the boundary maps of the cellular chain complex over F_2, k = 2 - chi = 470, d_Z is the shortest homologically nontrivial cycle of the map and d_X that of the dual map. Found in a census of regular maps (normal subgroups of the triangle groups <r,s | r^p, s^q, (rs)2>, Magma's LowIndexNormalSubgroups). The qubit order is that of the dart permutations in the public package in the references (data/maps.json), whose src/rebuild.py rebuilds these matrices from them and from the presentation.
model Claude Claude Opus 5.5 (claimed, not verified)
builds on https://arxiv.org/abs/1506.04029, https://www.math.auckland.ac.nz/~conder/ChiralMaps301.txt, https://github.com/TimoKellerMath/quantum-error-correction/tree/2e97a5361e7b9327128baa242bdedd333f7d7e12/hyperbolic-map-codes
date 2026-11-10
notes Exact distance d_X = d_Z = 6: tropidist (arXiv:2611.08247) at the board's pinned commit b03ec2d4077f closes both sides (certs/936-470-6.json, level solver); independently two exact programs for check matrices with column weight 2 and an enumeration of all circuits of length <= 6 (26364 X-type and 26364 Z-type logical operators of weight 6, none lighter), see the research note. Novelty: no board entry with these n and k at commit 8042f9da; parameters not found in Breuckmann and Terhal (arXiv:1506.04029), Breuckmann et al. (arXiv:1703.00590), Breuckmann's thesis (arXiv:1802.01520), Mahmoud and Rayan (arXiv:2610.10948), Breuckmann and Burton (arXiv:2202.06647), Mahmoud, Ali and Rayan (arXiv:2504.07800), the catalogs of QEC-pages (Quantum_LDPC_Codes) and qecdb.org; Conder's lists contain the map, not the code. Equivalence with existing entries: checked, none has these n and k.
family topological (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

[[936,470,6]]: chiral {8,8} surface code, Conder's map C235.23

Direction & hypothesis

Cell: check weight 8, unrestricted locality (no layout submitted). Surface codes of regular maps of type {p,q} on closed hyperbolic surfaces (Breuckmann and Terhal, arXiv:1506.04029) have k = 2 - chi = (1 - 2/p - 2/q) n + 2, so {8,8} maps give k/n close to 1/2 at check weight 8, while the distance is the systole of the map (of the dual map for d_X) and grows only logarithmically in n. At board commit 8042f9da the entries of check weight at most 8 with d = 6 and the largest kd^2/n were the lifted-product codes [[780,318,6]] to [[1000,406,6]], kd^2/n about 14.6. Hypothesis: {8,8} maps whose systoles reach 6 dominate them, at kd^2/n about 18.

What was searched

A census of all regular maps of type {p,q}, 3 <= p,q <= 8, 1/p + 1/q < 1/2, with at most 2000 edges (chiral {8,8} maps up to 1000 edges): the normal subgroups of index 2E of the triangle groups <r,s | r^p, s^q, (rs)^2> in which r, s, rs keep their orders (Magma's LowIndexNormalSubgroups), the non-orientable maps from the extended triangle groups, and 2000 cyclic covers of the orientable maps with n <= 1000 (random voltage classes, seeds recorded). In total 2174 orientable and 340 non-orientable maps (up to duality and mirror image) and 2000 covers, 7063 codes with their X/Z duals, each with exact d_X and d_Z by the programs below. At board commit 8042f9da, 254 parameter points of the census were undominated; we submit nine of them, one per pull request, and left out the points we found in the literature: [[896,386,6]] ({7,7}) and [[960,194,8]] ({5,5}) are data points of Fig. 3.7 of Breuckmann's thesis (arXiv:1802.01520), [[588,254,6]] and [[273,119,5]] are in its Table 3.1. This code is the chiral {8,8} map C235.23 of M. Conder's list (census orientation: its mirror image, same code). It is one of two {8,8} maps of the census with 936 edges and d = 6; we submit the first. Sources checked without finding it: Breuckmann and Terhal (arXiv:1506.04029), Breuckmann et al. (arXiv:1703.00590), Breuckmann's thesis (arXiv:1802.01520), Mahmoud and Rayan (arXiv:2610.10948), Breuckmann and Burton (arXiv:2202.06647), Mahmoud, Ali and Rayan (arXiv:2504.07800), the catalogs of QEC-pages (Quantum_LDPC_Codes) and qecdb.org; Conder's lists contain the maps, not the codes.

Evidence trail

  • k = 470 = 936 - 233 - 233 (ranks over GF(2)) = 2 - chi; H_X H_Z^T = 0; every qubit lies in two X-checks and two Z-checks, so both sides are graph-like (computed).
  • Upper bound: an X-type and a Z-type logical operator of weight 6, in the entry.
  • Lower bound, exact, by four computations: (1) graphlike_A, shortest cycles with logical annotations in F_2^k; (2) graphlike_B, shortest paths in the double covers of the check graph given by the logical operators, written independently; their exactness is proved in github.com/TimoKellerMath/quantum-error-correction @ 2e97a5361e7b9327128baa242bdedd333f7d7e12, hyperbolic-map-codes/src/graphlike_A/NOTES.md and hyperbolic-map-codes/src/graphlike_B/NOTES.md, and they agree on all 7063 census codes; (3) an enumeration of all circuits of length at most 6 with a row-space test: the graph of the map and its dual have no circuit shorter than 6, and all 26364 circuits of length 6 are nontrivial, on both sides; (4) tropidist (Cheng, Guo and Pan, arXiv:2611.08247) at the board's pinned commit b03ec2d4077f, one thread, 600 s limit, on the board's css-sides problems: exact 6 and 6 in 2.6 s and 2.7 s, recorded in certs/936-470-6.json.
  • Final claim: d_X = d_Z = 6, exact (computer-assisted; the four computations agree). 26364 X-type and 26364 Z-type logical operators have weight 6.

Dead ends

  • Within the census no {8,8}, {6,6} or {7,7} map reaches d = 7; d >= 7 occurs only for {3,7}, {4,5}, {4,6} and {5,5} (n <= 2000).
  • Among the 1005 {8,8} maps of the census (up to mirror image), 19 have d = 6 (from n = 640 on) and none more; 937 have d = 2 or 4.

Tools

Claude Opus 5.5 (Claude Code). Magma V2.30 for the census (LowIndexNormalSubgroups, coset actions, the presentations and Conder's names); Python for the map codes; the C programs graphlike_A and graphlike_B and the Python circuit enumeration, all in the public package below; tropidist b03ec2d4077f. The largest Magma run of the census (orientable {6,6} maps, index at most 4000) took 33 CPU minutes; exact distances of all 7063 codes took 46 s with graphlike_A and 76 s with graphlike_B.

Reproduction

G = <r,s | r^8, s^8, (r*s)^2, s*r*s^-2*r^-3*s^-2*r*s*r^-1, s^-1*r^-1*s*r^-1*s*r^-2*s^-1*r*s^-1*r*s^-1> (order 1872); qubits = edges {g, grs}, X-checks = vertices g<s>, Z-checks = faces g<r>, incidences mod 2. In hyperbolic-map-codes/ of github.com/TimoKellerMath/quantum-error-correction @ 2e97a5361e7b: make check runs hyperbolic-map-codes/src/rebuild.py (standard library), which rebuilds these matrices from the stored darts and from the presentation, checks Conder's relators, k and the witnesses; make distances runs graphlike_A, graphlike_B and the circuit enumeration; make tropidist-inputs writes the tropidist problems.

Parity checks

X-checks 234 (max weight 8) · Z-checks 234 (max weight 8)
H_X (234 checks, sparse supports)
[0, 2, 3, 7, 10, 19, 27, 47] [0, 1, 5, 13, 15, 34, 39, 81] [2, 6, 8, 17, 22, 43, 55, 102] [1, 4, 12, 30, 32, 72, 77, 164] [7, 18, 20, 45, 50, 106, 116, 151] [8, 21, 23, 53, 58, 123, 132, 256] [3, 9, 25, 61, 63, 140, 144, 294] [4, 11, 29, 68, 70, 155, 160, 314] [13, 33, 35, 79, 84, 134, 180, 188] [5, 14, 37, 88, 90, 197, 201, 394] [6, 16, 41, 96, 98, 213, 217, 418] [19, 46, 48, 108, 111, 234, 241, 408] [20, 49, 51, 114, 119, 247, 254, 466] [22, 54, 56, 68, 124, 128, 154, 156] [23, 28, 57, 107, 134, 231, 282, 444] [9, 24, 60, 136, 138, 198, 290, 354] [10, 26, 65, 146, 148, 303, 305, 537] [11, 28, 67, 151, 153, 308, 312, 542] [30, 58, 71, 73, 131, 133, 162, 167] [12, 31, 75, 171, 173, 344, 348, 605] [34, 80, 82, 181, 184, 283, 364, 371] [35, 44, 83, 85, 103, 191, 224, 381] [14, 36, 87, 193, 195, 345, 390, 573] [15, 38, 92, 203, 205, 403, 405, 671] [16, 40, 95, 141, 207, 209, 211, 415] [17, 42, 100, 163, 220, 346, 430, 699] [18, 44, 104, 225, 227, 437, 439, 708] [47, 86, 109, 168, 237, 337, 454, 561] [48, 110, 112, 239, 244, 311, 464, 550] [50, 115, 117, 202, 209, 250, 400, 411] [51, 94, 118, 192, 256, 384, 482, 568] [21, 52, 121, 259, 261, 367, 487, 630] [55, 125, 126, 266, 269, 490, 496, 674] [56, 127, 129, 272, 275, 385, 447, 650] [24, 59, 135, 283, 285, 451, 517, 649] [61, 139, 141, 191, 292, 295, 380, 382] [25, 62, 75, 121, 172, 260, 310, 548] [26, 64, 145, 228, 301, 529, 534, 543] [27, 66, 150, 235, 307, 450, 541, 599] [29, 69, 158, 251, 320, 322, 467, 568] [72, 163, 165, 329, 332, 383, 581, 586] [73, 78, 166, 168, 177, 338, 356, 594] [31, 74, 170, 340, 342, 566, 602, 775] [32, 76, 175, 350, 352, 503, 612, 614] [33, 78, 178, 357, 359, 619, 621, 829] [81, 169, 182, 317, 367, 559, 631, 769] [82, 183, 185, 229, 232, 369, 373, 445] [84, 136, 187, 189, 233, 286, 349, 377] [59, 85, 102, 190, 267, 339, 492, 597] [36, 86, 192, 383, 385, 628, 651, 815] [88, 196, 198, 338, 392, 395, 593, 595] [37, 41, 89, 97, 158, 277, 321, 423] [38, 91, 202, 360, 401, 513, 663, 668] [39, 93, 207, 365, 407, 627, 675, 789] [40, 94, 208, 408, 410, 515, 616, 678] [96, 119, 212, 214, 253, 255, 417, 421] [42, 99, 218, 315, 425, 427, 555, 557] [43, 101, 222, 387, 432, 434, 653, 705] [45, 105, 200, 229, 397, 441, 562, 788] [46, 107, 142, 232, 446, 595, 714, 814] [109, 236, 238, 452, 457, 517, 668, 677] [83, 111, 186, 240, 242, 344, 431, 641] [112, 149, 223, 243, 299, 466, 531, 726] [49, 113, 197, 269, 393, 469, 495, 632] [116, 248, 249, 379, 473, 475, 647, 730] [117, 166, 184, 251, 306, 334, 370, 539] [52, 120, 150, 214, 258, 420, 485, 586] [53, 80, 122, 199, 263, 489, 741, 786] [54, 114, 246, 428, 471, 729, 742, 881] [126, 159, 268, 270, 323, 494, 498, 569] [128, 145, 242, 273, 300, 420, 461, 688] [129, 135, 257, 274, 284, 348, 444, 609] [57, 130, 237, 277, 453, 455, 506, 591] [132, 278, 279, 507, 509, 540, 602, 752] [133, 280, 281, 285, 375, 512, 516, 666] [60, 137, 250, 288, 455, 477, 520, 665] [127, 140, 271, 293, 456, 509, 577, 753] [62, 142, 296, 457, 508, 528, 672, 720] [63, 143, 298, 319, 491, 563, 727, 790] [64, 93, 206, 238, 406, 443, 456, 550] [146, 155, 302, 315, 415, 535, 556, 596] [65, 113, 147, 178, 245, 288, 358, 468] [66, 99, 149, 306, 323, 493, 552, 694] [67, 152, 310, 378, 492, 547, 549, 639] [156, 161, 316, 317, 326, 560, 575, 785] [69, 157, 319, 496, 562, 564, 713, 773] [70, 159, 255, 278, 324, 480, 481, 571] [71, 161, 327, 501, 528, 576, 578, 702] [164, 217, 318, 330, 544, 750, 767, 805] [122, 165, 262, 331, 333, 361, 584, 588] [167, 193, 216, 335, 336, 363, 386, 569] [74, 169, 247, 339, 472, 596, 719, 803] [171, 343, 345, 560, 604, 606, 784, 786] [76, 174, 279, 349, 508, 510, 579, 610] [77, 176, 354, 432, 582, 616, 703, 802] [79, 179, 293, 347, 361, 623, 770, 894] [182, 366, 368, 510, 516, 629, 633, 651] [185, 206, 224, 355, 372, 399, 665, 839] [188, 375, 376, 592, 642, 644, 813, 841] [189, 316, 332, 378, 406, 558, 585, 673] [87, 194, 261, 377, 388, 646, 654, 823] [89, 199, 268, 396, 633, 662, 827, 836] [90, 200, 236, 398, 546, 733, 771, 840] [91, 176, 264, 353, 368, 445, 615, 632] [203, 290, 308, 402, 521, 543, 669, 787] [92, 186, 204, 327, 374, 388, 577, 640] [95, 210, 413, 461, 531, 549, 681, 682] [213, 280, 358, 397, 419, 655, 694, 852] [97, 215, 422, 538, 619, 663, 745, 856] [98, 170, 216, 341, 424, 600, 692, 817] [100, 104, 219, 226, 271, 413, 479, 710] [101, 174, 221, 262, 325, 431, 572, 796] [103, 157, 223, 318, 435, 561, 707, 787] [147, 225, 244, 436, 463, 465, 643, 664] [105, 228, 295, 440, 525, 526, 620, 667] [106, 230, 313, 544, 553, 696, 768, 777] [108, 233, 291, 429, 447, 522, 701, 762] [160, 235, 325, 449, 451, 573, 716, 779] [110, 172, 346, 475, 497, 607, 721, 732] [152, 241, 309, 459, 460, 546, 724, 770] [115, 239, 458, 637, 723, 879, 882, 896] [249, 301, 414, 474, 476, 533, 618, 731] [118, 252, 450, 479, 605, 717, 736, 869] [181, 254, 304, 363, 391, 538, 656, 853] [120, 257, 407, 483, 553, 674, 676, 776] [259, 275, 433, 486, 502, 503, 661, 739] [123, 264, 287, 459, 519, 675, 707, 779] [124, 143, 265, 297, 340, 464, 580, 598] [125, 153, 215, 311, 382, 551, 648, 774] [267, 491, 493, 534, 678, 744, 745, 777] [221, 270, 330, 472, 497, 583, 650, 804] [154, 252, 313, 478, 500, 554, 662, 778] [130, 222, 276, 371, 433, 505, 635, 697] [131, 272, 499, 590, 748, 783, 812, 900] [162, 218, 328, 393, 426, 567, 697, 873] [201, 208, 281, 399, 409, 504, 511, 542] [282, 350, 390, 513, 611, 655, 704, 825] [180, 248, 362, 410, 514, 532, 677, 756] [137, 287, 352, 613, 656, 813, 886, 913] [138, 289, 343, 460, 486, 603, 638, 725] [139, 291, 342, 485, 601, 738, 772, 895] [294, 511, 519, 524, 621, 757, 889, 923] [260, 437, 480, 529, 701, 709, 765, 781] [144, 299, 314, 483, 514, 545, 737, 755] [183, 243, 303, 321, 462, 536, 644, 843] [148, 304, 478, 484, 626, 684, 735, 884] [320, 565, 566, 699, 768, 792, 793, 893] [333, 353, 356, 574, 587, 609, 823, 910] [230, 336, 442, 470, 556, 591, 615, 780] [173, 347, 366, 505, 608, 751, 844, 911] [175, 334, 351, 469, 554, 589, 600, 810] [177, 309, 355, 434, 545, 617, 704, 769] [204, 357, 373, 618, 637, 638, 811, 822] [179, 360, 395, 622, 659, 660, 799, 824] [312, 365, 552, 626, 628, 705, 775, 833] [187, 369, 634, 808, 838, 887, 921, 922] [289, 376, 401, 643, 645, 667, 798, 842] [190, 245, 379, 467, 627, 764, 834, 847] [329, 381, 404, 580, 603, 672, 818, 918] [194, 387, 571, 736, 795, 818, 878, 900] [195, 212, 389, 416, 565, 635, 791, 809] [196, 211, 391, 414, 465, 564, 683, 864] [274, 394, 501, 653, 658, 848, 886, 924] [331, 372, 403, 548, 636, 670, 812, 912] [205, 210, 404, 412, 522, 647, 846, 923] [266, 400, 416, 666, 684, 740, 832, 861] [418, 439, 680, 686, 755, 858, 884, 928] [246, 263, 419, 470, 488, 658, 687, 854] [265, 421, 425, 438, 533, 689, 690, 695] [423, 555, 587, 612, 742, 807, 826, 861] [219, 428, 474, 498, 530, 601, 700, 747] [220, 429, 449, 702, 751, 859, 880, 929] [226, 297, 362, 487, 521, 624, 761, 796] [227, 422, 438, 634, 691, 711, 837, 870] [231, 412, 443, 541, 582, 680, 713, 803] [234, 448, 669, 679, 834, 857, 858, 901] [409, 454, 614, 676, 719, 741, 859, 878] [240, 452, 502, 718, 877, 889, 921, 931] [442, 476, 539, 551, 642, 686, 733, 865] [298, 411, 462, 530, 679, 734, 759, 860] [253, 370, 629, 743, 835, 868, 885, 924] [417, 440, 607, 685, 712, 778, 863, 898] [284, 430, 435, 481, 515, 631, 706, 735] [482, 557, 572, 575, 692, 776, 781, 871] [258, 322, 484, 567, 583, 687, 794, 866] [273, 463, 494, 746, 793, 883, 904, 905] [427, 436, 500, 570, 698, 738, 749, 862] [276, 307, 326, 504, 540, 574, 750, 797] [506, 512, 527, 671, 683, 724, 754, 887] [364, 518, 625, 757, 758, 825, 890, 920] [286, 398, 518, 636, 664, 759, 845, 850] [477, 720, 731, 819, 890, 891, 894, 927] [292, 523, 536, 622, 730, 760, 831, 883] [446, 499, 524, 624, 645, 673, 763, 844] [380, 448, 585, 690, 715, 722, 804, 869] [526, 593, 625, 726, 764, 780, 832, 837] [296, 359, 527, 620, 734, 806, 830, 909] [300, 507, 532, 715, 725, 874, 880, 912] [302, 441, 594, 613, 791, 827, 902, 934] [537, 547, 691, 756, 772, 773, 888, 896] [305, 384, 617, 648, 649, 805, 828, 846] [324, 473, 558, 570, 641, 782, 790, 899] [351, 576, 588, 700, 798, 808, 809, 906] [328, 579, 606, 747, 800, 820, 821, 898] [335, 584, 698, 728, 739, 806, 868, 876] [389, 488, 590, 610, 693, 749, 811, 824] [337, 374, 592, 639, 758, 802, 855, 914] [341, 599, 706, 774, 847, 881, 897, 902] [581, 652, 752, 801, 848, 849, 877, 925] [386, 608, 652, 685, 807, 822, 850, 916] [646, 836, 842, 873, 891, 903, 925, 926] [392, 657, 670, 718, 723, 800, 841, 851] [660, 761, 762, 784, 801, 839, 855, 909] [396, 578, 661, 695, 799, 845, 872, 908] [402, 623, 732, 785, 795, 895, 931, 932] [405, 597, 737, 797, 814, 815, 907, 913] [657, 681, 788, 856, 862, 892, 901, 927] [424, 688, 693, 721, 860, 867, 870, 926] [426, 611, 696, 843, 864, 885, 897, 930] [563, 708, 714, 789, 828, 874, 914, 932] [458, 471, 709, 722, 728, 792, 875, 903] [525, 710, 817, 866, 882, 899, 908, 917] [453, 559, 589, 716, 783, 849, 919, 933] [468, 659, 682, 727, 863, 865, 875, 922] [630, 729, 767, 782, 833, 915, 929, 935] [489, 703, 740, 771, 829, 907, 930, 933] [490, 535, 717, 743, 766, 816, 867, 915] [495, 744, 754, 831, 879, 920, 928, 934] [520, 640, 711, 760, 763, 820, 840, 876] [523, 598, 765, 794, 816, 892, 906, 916] [712, 753, 857, 871, 888, 905, 918, 935] [604, 746, 748, 819, 826, 835, 838, 917] [766, 821, 852, 853, 872, 893, 910, 919] [654, 689, 810, 830, 851, 854, 904, 911]
H_Z (234 checks, sparse supports)
[0, 1, 2, 4, 8, 11, 23, 28] [2, 6, 7, 16, 20, 40, 51, 94] [0, 3, 9, 13, 24, 35, 59, 85] [1, 5, 14, 30, 36, 73, 86, 168] [7, 18, 19, 44, 48, 103, 112, 223] [8, 21, 22, 52, 56, 120, 129, 257] [3, 10, 26, 61, 64, 93, 141, 207] [4, 12, 31, 68, 74, 156, 169, 317] [13, 33, 34, 78, 82, 177, 185, 355] [5, 15, 38, 88, 91, 176, 198, 354] [6, 17, 42, 66, 96, 99, 150, 214] [19, 46, 47, 107, 109, 231, 238, 443] [20, 49, 50, 113, 117, 245, 251, 467] [22, 54, 55, 114, 126, 247, 270, 472] [23, 57, 58, 130, 133, 276, 281, 504] [9, 25, 46, 62, 108, 136, 142, 233] [10, 27, 66, 146, 149, 155, 299, 314] [11, 29, 69, 106, 151, 157, 318, 544] [30, 71, 72, 161, 165, 326, 333, 574] [12, 32, 76, 171, 174, 325, 345, 573] [34, 53, 80, 81, 123, 182, 264, 368] [35, 83, 84, 186, 189, 374, 378, 639] [14, 37, 80, 89, 181, 193, 199, 363] [15, 39, 93, 203, 206, 308, 399, 542] [16, 41, 97, 125, 209, 215, 266, 400] [17, 43, 72, 101, 163, 164, 221, 330] [18, 26, 45, 65, 105, 147, 225, 228] [27, 47, 86, 192, 235, 384, 451, 649] [48, 110, 111, 172, 242, 310, 461, 549] [50, 115, 116, 239, 249, 311, 476, 551] [51, 118, 119, 252, 255, 478, 481, 735] [21, 53, 101, 122, 222, 259, 262, 433] [55, 102, 125, 153, 267, 312, 493, 552] [56, 127, 128, 242, 271, 344, 479, 605] [58, 131, 132, 272, 279, 385, 510, 651] [28, 67, 134, 152, 180, 309, 514, 545] [24, 60, 137, 283, 287, 364, 519, 757] [61, 139, 140, 210, 271, 291, 413, 522] [25, 63, 143, 260, 297, 521, 529, 543] [68, 154, 155, 313, 315, 553, 557, 776] [29, 70, 159, 320, 323, 552, 566, 775] [73, 166, 167, 334, 336, 453, 589, 591] [31, 75, 163, 172, 329, 340, 346, 580] [32, 77, 176, 282, 350, 353, 444, 609] [33, 38, 79, 92, 179, 204, 357, 360] [39, 81, 169, 339, 365, 597, 628, 815] [82, 117, 183, 184, 250, 277, 321, 455] [84, 187, 188, 232, 369, 376, 446, 645] [85, 190, 191, 379, 382, 647, 648, 846] [36, 87, 194, 383, 387, 581, 653, 848] [88, 113, 137, 196, 197, 288, 391, 656] [37, 90, 97, 200, 397, 513, 655, 663] [40, 95, 210, 234, 408, 412, 680, 858] [96, 212, 213, 416, 419, 484, 684, 687] [41, 98, 216, 315, 336, 423, 555, 556] [42, 54, 100, 124, 219, 265, 425, 428] [43, 59, 102, 135, 284, 432, 515, 616] [44, 83, 104, 226, 248, 362, 473, 641] [45, 106, 213, 230, 397, 418, 442, 686] [90, 109, 201, 236, 237, 399, 455, 665] [111, 240, 241, 452, 460, 532, 677, 725] [112, 243, 244, 298, 319, 462, 465, 564] [49, 114, 230, 246, 313, 469, 470, 554] [116, 151, 248, 308, 410, 534, 543, 678] [119, 253, 254, 306, 323, 363, 370, 569] [94, 123, 208, 256, 407, 409, 675, 676] [52, 121, 260, 278, 300, 420, 480, 507] [89, 126, 158, 268, 269, 322, 393, 567] [128, 154, 159, 273, 324, 494, 500, 570] [129, 274, 275, 501, 503, 614, 702, 859] [57, 107, 232, 264, 445, 459, 506, 724] [70, 132, 160, 256, 278, 325, 482, 572] [133, 162, 197, 280, 393, 394, 419, 658] [134, 188, 282, 285, 375, 513, 517, 668] [136, 198, 286, 395, 518, 660, 758, 855] [60, 138, 289, 401, 457, 477, 668, 720] [79, 140, 180, 293, 294, 362, 524, 624] [141, 209, 295, 411, 526, 679, 764, 834] [62, 75, 173, 279, 293, 347, 508, 509] [63, 144, 267, 299, 491, 492, 531, 549] [64, 145, 300, 456, 532, 753, 756, 888] [69, 146, 158, 302, 303, 321, 441, 562] [65, 148, 304, 358, 493, 538, 694, 745] [67, 153, 311, 443, 547, 550, 713, 773] [124, 156, 297, 316, 487, 558, 630, 782] [71, 76, 162, 175, 328, 351, 576, 579] [77, 164, 318, 454, 561, 582, 719, 803] [121, 165, 189, 261, 331, 332, 377, 548] [122, 131, 167, 263, 335, 488, 584, 590] [168, 337, 338, 592, 595, 813, 814, 913] [74, 170, 341, 450, 535, 596, 599, 717] [171, 186, 194, 343, 344, 388, 603, 818] [78, 166, 178, 280, 358, 375, 539, 642] [173, 182, 261, 348, 366, 367, 609, 823] [184, 370, 371, 416, 516, 629, 635, 666] [185, 372, 373, 398, 460, 546, 636, 638] [191, 380, 381, 406, 464, 550, 580, 585] [193, 345, 386, 606, 652, 821, 849, 919] [87, 195, 389, 510, 610, 633, 646, 836] [91, 202, 400, 495, 512, 632, 666, 754] [152, 203, 310, 402, 403, 548, 623, 770] [92, 205, 238, 404, 456, 457, 577, 672] [95, 211, 301, 414, 534, 681, 745, 856] [214, 420, 421, 688, 690, 717, 867, 869] [98, 217, 322, 330, 482, 568, 583, 692] [99, 218, 426, 694, 696, 768, 852, 893] [100, 220, 226, 429, 572, 701, 781, 796] [103, 224, 337, 355, 561, 617, 828, 914] [225, 436, 437, 570, 709, 727, 790, 875] [104, 227, 295, 380, 438, 525, 690, 710] [105, 115, 202, 229, 373, 401, 637, 667] [108, 234, 437, 448, 701, 708, 715, 874] [220, 235, 284, 348, 430, 449, 450, 605] [237, 287, 352, 453, 454, 614, 716, 779] [110, 239, 448, 458, 679, 721, 722, 860] [241, 290, 354, 408, 459, 616, 707, 787] [145, 244, 265, 273, 301, 463, 464, 533] [190, 223, 247, 339, 435, 466, 706, 847] [219, 249, 413, 474, 475, 607, 682, 863] [250, 411, 414, 477, 527, 683, 731, 734] [251, 320, 334, 341, 565, 600, 791, 902] [118, 192, 385, 472, 650, 719, 736, 878] [211, 254, 391, 415, 466, 556, 726, 780] [255, 346, 417, 480, 607, 699, 709, 792] [120, 258, 484, 490, 626, 674, 833, 915] [259, 486, 487, 624, 725, 751, 844, 880] [269, 495, 496, 564, 696, 744, 777, 864] [170, 270, 342, 424, 497, 498, 601, 721] [127, 161, 272, 316, 327, 499, 577, 673] [174, 233, 240, 275, 349, 431, 447, 502] [231, 257, 307, 444, 483, 541, 737, 797] [130, 277, 350, 423, 426, 611, 612, 697] [281, 405, 511, 512, 621, 671, 829, 907] [222, 283, 371, 390, 434, 451, 573, 704] [135, 274, 285, 516, 651, 815, 886, 913] [138, 224, 290, 381, 521, 603, 761, 839] [139, 143, 292, 298, 523, 530, 598, 601] [144, 294, 519, 675, 714, 737, 789, 814] [207, 407, 415, 496, 596, 674, 713, 803] [142, 296, 392, 403, 527, 595, 670, 671] [228, 440, 529, 712, 765, 857, 892, 901] [215, 292, 303, 382, 422, 536, 537, 691] [147, 288, 376, 520, 536, 643, 644, 760] [148, 305, 365, 384, 467, 568, 626, 627] [149, 243, 306, 539, 551, 774, 843, 897] [150, 307, 383, 540, 586, 602, 628, 775] [160, 314, 435, 545, 631, 707, 769, 779] [317, 559, 560, 741, 783, 786, 878, 900] [157, 319, 563, 627, 669, 787, 789, 834] [291, 332, 447, 485, 585, 586, 650, 804] [333, 505, 587, 588, 608, 635, 807, 809] [229, 338, 441, 445, 593, 594, 615, 780] [340, 566, 598, 793, 816, 905, 915, 935] [175, 352, 368, 469, 613, 632, 633, 827] [177, 356, 559, 574, 769, 797, 907, 933] [357, 422, 476, 618, 619, 711, 733, 840] [178, 359, 395, 468, 526, 593, 620, 659] [179, 187, 349, 361, 588, 610, 808, 824] [181, 364, 538, 619, 625, 740, 829, 832] [367, 387, 481, 571, 630, 631, 705, 833] [183, 369, 462, 518, 625, 634, 759, 837] [286, 289, 377, 486, 646, 661, 842, 845] [378, 547, 558, 563, 772, 790, 895, 932] [195, 356, 390, 594, 655, 791, 852, 910] [196, 200, 392, 398, 465, 657, 664, 788] [201, 394, 409, 432, 489, 653, 703, 741] [199, 396, 503, 604, 612, 661, 786, 826] [360, 622, 663, 831, 856, 890, 920, 927] [204, 388, 590, 654, 670, 811, 812, 851] [205, 405, 412, 492, 582, 597, 639, 802] [206, 372, 406, 446, 673, 714, 874, 912] [208, 410, 511, 517, 649, 677, 846, 923] [212, 216, 386, 389, 417, 424, 685, 693] [217, 418, 541, 599, 648, 680, 774, 805] [246, 253, 421, 471, 689, 728, 854, 868] [425, 555, 695, 766, 807, 816, 872, 916] [218, 328, 335, 427, 498, 569, 698, 747] [221, 324, 431, 497, 571, 641, 732, 795] [227, 439, 531, 682, 686, 726, 837, 865] [236, 374, 452, 592, 640, 718, 840, 841] [461, 681, 688, 691, 738, 772, 862, 870] [245, 379, 468, 491, 727, 730, 744, 831] [402, 404, 475, 647, 669, 732, 857, 918] [252, 479, 692, 710, 712, 778, 817, 871] [258, 427, 485, 557, 738, 765, 781, 794] [433, 697, 739, 848, 868, 873, 924, 925] [262, 361, 560, 623, 761, 784, 785, 796] [263, 353, 470, 489, 587, 615, 740, 861] [351, 428, 600, 700, 742, 817, 826, 917] [266, 490, 742, 743, 861, 881, 885, 897] [268, 494, 743, 746, 835, 836, 867, 926] [396, 488, 500, 662, 687, 749, 866, 908] [276, 449, 505, 540, 716, 751, 752, 849] [442, 506, 591, 683, 733, 771, 864, 930] [342, 509, 575, 602, 753, 785, 871, 895] [312, 434, 504, 542, 617, 705, 750, 805] [305, 439, 514, 537, 708, 755, 756, 828] [359, 520, 524, 621, 665, 763, 839, 909] [508, 579, 718, 720, 800, 877, 891, 925] [296, 528, 576, 645, 798, 830, 844, 911] [302, 304, 478, 535, 662, 766, 827, 853] [430, 544, 699, 706, 729, 767, 768, 881] [309, 546, 703, 704, 758, 771, 802, 825] [562, 773, 788, 858, 879, 896, 901, 928] [326, 575, 676, 750, 767, 776, 859, 929] [327, 578, 606, 640, 660, 784, 799, 820] [329, 429, 528, 581, 672, 702, 762, 801] [331, 584, 636, 652, 801, 806, 850, 909] [343, 347, 604, 608, 638, 819, 822, 894] [366, 589, 629, 748, 783, 810, 835, 911] [611, 613, 644, 813, 825, 843, 920, 934] [501, 578, 654, 658, 823, 854, 872, 910] [436, 438, 664, 695, 698, 711, 845, 876] [458, 463, 643, 723, 842, 851, 903, 904] [523, 525, 622, 667, 798, 799, 906, 908] [440, 533, 618, 620, 685, 689, 822, 830] [554, 778, 793, 810, 821, 893, 898, 904] [471, 583, 722, 729, 782, 804, 866, 899] [634, 637, 693, 811, 838, 870, 882, 917] [473, 730, 882, 883, 888, 896, 899, 905] [474, 731, 746, 747, 760, 819, 820, 883] [530, 700, 728, 734, 806, 808, 875, 922] [715, 736, 818, 869, 880, 918, 929, 935] [483, 515, 553, 678, 735, 755, 777, 884] [499, 502, 739, 748, 763, 838, 876, 921] [565, 567, 792, 794, 809, 873, 903, 906] [724, 757, 770, 887, 889, 890, 894, 921] [507, 752, 795, 812, 877, 900, 912, 931] [656, 853, 885, 886, 919, 924, 930, 933] [522, 762, 855, 889, 914, 923, 931, 932] [684, 764, 832, 847, 884, 902, 928, 934] [657, 659, 749, 800, 824, 862, 863, 898] [642, 723, 754, 841, 865, 879, 887, 922] [759, 850, 860, 891, 892, 916, 926, 927]
Code ID 936-470-6 · download JSON · raw on GitHub