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[[1000,502,6]] d =
n
1000
k
502
d
6
kd²/n
18.072
w
8
X/Z
1

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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, 3, 8, 10, 66, 121]
d_Z 6 · witness weight 6 (claimed exact)
witness operator (support, 6 qubits)
[0, 1, 4, 7, 29, 106]
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)×1000 (2,2)×7000 (3,2)×49000 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,2): 1000 (2,2): 7000 (3,2): 49000 (3,4): 14000
trapping sets H_Z (1,2)×1000 (2,2)×7000 (3,2)×49000 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,2): 1000 (2,2): 7000 (3,2): 49000 (3,4): 14000

Construction & provenance

authors @TimoKellerMath
provenance submitted through the challenge
novelty new parameter set claimed by submitter
construction Surface code of the orientably-regular map C251.45 of type {8,8} (genus 251) 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, r-1*s3*r-3*s2*r-1*s*r-1, s2*r-2*s*r-2*s*r-1*s2*r-1> of order 2000. Darts = elements of G (right multiplication), faces = cosets g<r>, vertices = cosets g<s>, edges = cosets g<rs> = {g, grs}. Qubits on the 1000 edges, X-checks on the 250 vertices (weight 8), Z-checks on the 250 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 = 502, 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/1000-502-6.json, level solver); independently two exact programs for check matrices with column weight 2 and an enumeration of all circuits of length <= 6 (22500 X-type and 22500 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

[[1000,502,6]]: chiral {8,8} surface code, Conder's map C251.45

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 C251.45 of M. Conder's list (census orientation: its mirror image, same code). It is one of six {8,8} maps of the census with 1000 edges and d = 6 (two of them dual to each other); 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 = 502 = 1000 - 249 - 249 (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 22500 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 2.9 s and 2.7 s, recorded in certs/1000-502-6.json.
  • Final claim: d_X = d_Z = 6, exact (computer-assisted; the four computations agree). 22500 X-type and 22500 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, r^-1*s^3*r^-3*s^2*r^-1*s*r^-1, s^2*r^-2*s*r^-2*s*r^-1*s^2*r^-1> (order 2000); 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 250 (max weight 8) · Z-checks 250 (max weight 8)
H_X (250 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, 169] [7, 18, 20, 45, 50, 106, 117, 245] [8, 21, 23, 53, 58, 124, 135, 281] [3, 9, 25, 61, 63, 143, 148, 317] [4, 11, 29, 68, 70, 160, 165, 345] [13, 33, 35, 79, 84, 185, 196, 397] [5, 14, 37, 88, 90, 205, 210, 434] [6, 16, 41, 96, 98, 223, 228, 464] [19, 46, 48, 108, 112, 202, 249, 509] [20, 49, 51, 91, 115, 120, 211, 262] [22, 54, 56, 126, 130, 203, 285, 561] [23, 28, 57, 133, 137, 298, 306, 472] [9, 24, 60, 139, 141, 311, 313, 595] [10, 26, 65, 151, 153, 329, 332, 612] [11, 28, 67, 156, 158, 336, 341, 620] [30, 71, 73, 167, 172, 294, 360, 371] [12, 31, 75, 176, 178, 285, 379, 383] [34, 80, 82, 187, 191, 377, 401, 726] [35, 83, 85, 179, 194, 199, 384, 414] [14, 36, 87, 201, 203, 428, 430, 760] [15, 38, 92, 213, 215, 446, 449, 777] [16, 40, 95, 219, 221, 456, 460, 640] [17, 42, 100, 231, 233, 400, 477, 702] [18, 44, 104, 239, 241, 491, 496, 626] [47, 109, 110, 251, 254, 474, 512, 830] [48, 111, 113, 214, 234, 256, 482, 517] [50, 116, 118, 264, 267, 475, 530, 781] [51, 94, 119, 150, 270, 272, 392, 712] [21, 52, 122, 275, 277, 425, 546, 633] [55, 127, 128, 140, 181, 287, 564, 837] [56, 64, 129, 131, 149, 215, 291, 570] [58, 134, 136, 141, 300, 303, 434, 643] [24, 59, 118, 138, 266, 268, 308, 534] [61, 142, 144, 315, 320, 335, 604, 617] [25, 62, 146, 323, 325, 524, 608, 746] [26, 64, 150, 326, 327, 432, 610, 764] [27, 66, 155, 200, 252, 426, 513, 757] [68, 119, 159, 161, 269, 343, 348, 633] [29, 69, 106, 163, 244, 352, 354, 651] [72, 168, 170, 362, 366, 647, 665, 920] [73, 171, 173, 355, 369, 374, 652, 676] [31, 74, 117, 175, 265, 376, 532, 688] [32, 76, 120, 180, 271, 386, 540, 702] [33, 78, 183, 391, 393, 577, 710, 715] [81, 188, 189, 272, 403, 406, 541, 729] [82, 154, 190, 192, 333, 387, 408, 733] [84, 195, 197, 327, 416, 419, 746, 948] [59, 85, 198, 212, 422, 424, 659, 913] [36, 86, 197, 200, 418, 420, 425, 748] [88, 204, 206, 305, 432, 437, 587, 769] [37, 89, 208, 440, 442, 740, 773, 928] [38, 91, 212, 443, 444, 691, 775, 940] [39, 93, 217, 375, 404, 686, 730, 936] [40, 94, 218, 293, 452, 454, 572, 782] [96, 159, 222, 224, 342, 462, 466, 631] [41, 97, 226, 469, 471, 530, 766, 796] [42, 99, 230, 315, 473, 475, 599, 800] [43, 101, 138, 235, 309, 483, 592, 808] [44, 103, 238, 403, 488, 728, 759, 957] [45, 105, 243, 284, 499, 501, 560, 816] [46, 107, 247, 504, 506, 555, 716, 824] [110, 178, 253, 484, 502, 514, 661, 831] [112, 165, 257, 519, 520, 718, 835, 950] [60, 113, 140, 237, 258, 276, 401, 548] [49, 114, 260, 523, 524, 666, 798, 980] [52, 121, 274, 368, 421, 543, 673, 751] [53, 123, 248, 279, 446, 553, 554, 754] [54, 125, 283, 352, 506, 558, 648, 649] [102, 209, 236, 486, 565, 792, 854, 962] [128, 152, 288, 289, 346, 514, 638, 639] [130, 292, 293, 571, 573, 616, 855, 865] [131, 230, 240, 273, 294, 474, 493, 574] [57, 132, 296, 308, 360, 577, 578, 663] [93, 135, 216, 220, 301, 533, 846, 961] [99, 136, 153, 229, 302, 304, 584, 798] [137, 221, 305, 307, 317, 373, 459, 588] [139, 310, 312, 410, 593, 597, 673, 864] [143, 270, 288, 316, 318, 538, 566, 600] [144, 247, 319, 321, 505, 585, 602, 873] [62, 145, 175, 367, 377, 606, 656, 672] [63, 147, 180, 242, 387, 433, 497, 704] [151, 328, 330, 430, 614, 669, 879, 899] [65, 152, 277, 331, 463, 518, 550, 788] [66, 154, 306, 544, 589, 839, 866, 943] [156, 198, 335, 337, 421, 464, 618, 622] [67, 157, 185, 339, 396, 452, 626, 628] [160, 280, 344, 346, 606, 635, 876, 886] [161, 243, 347, 349, 500, 629, 644, 888] [69, 162, 196, 290, 351, 417, 568, 646] [70, 164, 199, 356, 423, 612, 654, 754] [71, 166, 275, 358, 545, 547, 658, 660] [169, 363, 364, 424, 667, 669, 755, 922] [170, 216, 232, 365, 367, 450, 479, 655] [172, 370, 372, 444, 678, 681, 833, 928] [86, 173, 373, 385, 683, 685, 892, 992] [74, 174, 228, 372, 375, 680, 682, 930] [134, 176, 299, 378, 380, 581, 691, 694] [75, 177, 246, 382, 476, 698, 801, 924] [76, 179, 385, 558, 699, 700, 859, 945] [77, 181, 388, 499, 645, 668, 817, 905] [78, 182, 390, 667, 707, 783, 921, 938] [79, 105, 184, 242, 395, 498, 718, 720] [80, 186, 235, 241, 399, 484, 495, 723] [189, 256, 334, 354, 405, 516, 721, 893] [191, 341, 409, 735, 736, 829, 916, 960] [87, 97, 192, 202, 225, 389, 410, 665] [83, 193, 412, 570, 739, 740, 864, 895] [201, 427, 429, 456, 527, 672, 758, 762] [111, 205, 255, 422, 433, 435, 752, 765] [206, 292, 399, 436, 438, 724, 767, 971] [89, 207, 351, 596, 639, 647, 771, 891] [90, 209, 356, 394, 655, 692, 716, 909] [213, 265, 445, 447, 531, 779, 845, 977] [92, 98, 214, 227, 316, 448, 560, 734] [219, 258, 411, 455, 457, 737, 784, 980] [95, 220, 249, 289, 458, 508, 567, 693] [223, 450, 463, 465, 574, 713, 789, 867] [224, 381, 467, 562, 657, 696, 786, 922] [231, 313, 406, 476, 478, 678, 767, 927] [100, 232, 480, 578, 637, 705, 806, 963] [101, 234, 336, 619, 771, 807, 882, 974] [103, 204, 237, 431, 487, 536, 650, 763] [164, 239, 355, 455, 490, 492, 653, 812] [104, 240, 330, 494, 613, 749, 835, 934] [107, 246, 287, 418, 563, 822, 861, 983] [108, 186, 248, 398, 507, 529, 680, 826] [109, 250, 384, 551, 695, 708, 842, 883] [252, 357, 471, 648, 656, 827, 910, 932] [254, 416, 460, 553, 602, 745, 773, 856] [114, 157, 259, 338, 371, 522, 625, 679] [115, 261, 511, 526, 588, 742, 808, 841] [116, 263, 380, 528, 614, 693, 695, 843] [245, 481, 503, 624, 821, 869, 972, 987] [267, 331, 535, 536, 615, 709, 774, 933] [268, 342, 498, 505, 521, 630, 757, 823] [211, 236, 438, 485, 489, 636, 868, 895] [121, 273, 542, 586, 651, 707, 793, 941] [122, 276, 549, 601, 690, 853, 865, 908] [123, 278, 462, 552, 687, 787, 855, 981] [124, 218, 280, 453, 555, 763, 783, 978] [125, 251, 282, 511, 557, 594, 829, 834] [126, 284, 369, 582, 675, 730, 788, 921] [127, 286, 497, 562, 671, 694, 814, 942] [129, 290, 402, 435, 727, 766, 917, 997] [132, 193, 269, 295, 411, 537, 576, 738] [133, 297, 329, 405, 540, 563, 644, 851] [147, 281, 556, 840, 844, 848, 965, 987] [303, 585, 586, 723, 772, 870, 912, 946] [304, 397, 552, 559, 575, 722, 854, 860] [233, 278, 307, 481, 551, 590, 662, 917] [311, 376, 594, 596, 687, 689, 743, 937] [255, 312, 453, 515, 631, 725, 892, 955] [142, 282, 314, 382, 458, 598, 697, 739] [250, 302, 318, 510, 532, 601, 719, 951] [257, 320, 518, 589, 603, 605, 794, 833] [149, 321, 363, 556, 666, 857, 858, 888] [145, 238, 322, 489, 512, 605, 641, 715] [323, 423, 572, 583, 753, 866, 877, 967] [146, 324, 520, 545, 698, 727, 836, 984] [148, 162, 350, 642, 645, 789, 900, 902] [326, 522, 609, 688, 802, 818, 938, 939] [155, 168, 263, 334, 361, 393, 616, 714] [337, 395, 554, 579, 621, 623, 719, 868] [158, 253, 340, 374, 477, 684, 777, 890] [345, 531, 636, 637, 685, 873, 896, 935] [348, 641, 642, 700, 801, 899, 901, 959] [174, 349, 643, 653, 875, 903, 904, 982] [163, 328, 353, 398, 461, 611, 650, 878] [166, 357, 454, 592, 657, 816, 862, 896] [167, 184, 359, 394, 662, 717, 916, 918] [279, 364, 408, 451, 628, 732, 841, 919] [298, 366, 542, 598, 671, 785, 957, 993] [171, 262, 368, 487, 527, 674, 842, 924] [190, 260, 379, 407, 683, 692, 933, 941] [177, 381, 517, 625, 761, 886, 943, 989] [386, 417, 468, 701, 703, 747, 877, 966] [182, 378, 389, 483, 690, 706, 750, 887] [310, 340, 391, 629, 709, 711, 889, 949] [183, 392, 447, 713, 778, 861, 931, 960] [187, 361, 400, 664, 725, 745, 900, 956] [188, 229, 402, 467, 652, 797, 907, 964] [325, 404, 491, 549, 630, 809, 813, 891] [194, 300, 413, 513, 582, 728, 742, 963] [195, 415, 548, 649, 744, 779, 907, 965] [419, 448, 749, 750, 780, 911, 944, 994] [420, 617, 717, 724, 737, 880, 936, 954] [428, 473, 646, 759, 761, 799, 906, 926] [309, 407, 429, 591, 604, 731, 872, 875] [301, 409, 437, 583, 734, 768, 770, 959] [207, 390, 439, 547, 708, 729, 770, 884] [266, 286, 440, 533, 684, 934, 975, 999] [208, 222, 441, 461, 523, 580, 736, 838] [210, 338, 519, 600, 624, 834, 885, 990] [443, 568, 613, 738, 774, 804, 862, 951] [217, 344, 415, 451, 634, 660, 781, 914] [358, 457, 507, 566, 659, 703, 785, 825] [465, 485, 500, 590, 760, 790, 809, 818] [388, 466, 619, 677, 705, 791, 881, 948] [225, 370, 468, 496, 557, 677, 792, 858] [271, 469, 539, 793, 794, 850, 882, 977] [226, 442, 470, 510, 668, 710, 880, 989] [227, 472, 797, 843, 929, 954, 988, 991] [283, 478, 535, 559, 753, 802, 803, 905] [295, 383, 488, 575, 735, 765, 811, 985] [492, 611, 622, 795, 814, 845, 884, 885] [244, 365, 412, 502, 670, 782, 903, 994] [459, 504, 607, 711, 776, 786, 811, 966] [509, 775, 819, 828, 956, 958, 986, 995] [482, 503, 663, 748, 803, 820, 898, 919] [259, 521, 543, 567, 699, 778, 944, 997] [261, 525, 615, 812, 840, 920, 969, 998] [264, 529, 565, 608, 696, 751, 851, 923] [501, 525, 541, 819, 839, 852, 981, 999] [274, 436, 479, 544, 564, 627, 804, 838] [333, 494, 546, 722, 806, 815, 930, 953] [291, 526, 569, 618, 632, 810, 893, 978] [350, 561, 623, 847, 874, 889, 973, 991] [480, 490, 573, 609, 697, 752, 805, 849] [296, 431, 508, 701, 790, 827, 894, 946] [297, 427, 579, 658, 869, 911, 912, 996] [299, 486, 580, 744, 762, 810, 902, 950] [396, 534, 638, 674, 721, 847, 897, 979] [595, 621, 676, 815, 857, 910, 926, 976] [528, 587, 597, 682, 817, 836, 844, 915] [322, 515, 654, 679, 870, 908, 929, 975] [314, 339, 445, 627, 664, 776, 887, 976] [319, 353, 576, 733, 807, 846, 939, 984] [324, 516, 607, 832, 867, 872, 937, 940] [610, 826, 832, 837, 918, 925, 935, 998] [550, 620, 747, 823, 883, 904, 971, 995] [332, 362, 591, 634, 871, 894, 927, 990] [343, 359, 584, 632, 661, 828, 915, 993] [347, 414, 640, 706, 743, 878, 898, 964] [681, 704, 784, 787, 931, 932, 947, 979] [426, 670, 689, 756, 769, 923, 970, 973] [569, 726, 805, 863, 871, 945, 952, 988] [413, 741, 780, 850, 876, 949, 962, 986] [720, 741, 755, 800, 952, 961, 968, 983] [439, 537, 571, 731, 796, 822, 848, 890] [441, 538, 732, 772, 799, 859, 958, 970] [449, 635, 756, 853, 879, 881, 969, 985] [470, 758, 764, 795, 831, 953, 955, 968] [593, 599, 813, 820, 825, 852, 901, 909] [493, 714, 768, 791, 824, 913, 972, 982] [495, 603, 712, 860, 874, 914, 942, 992] [675, 830, 863, 925, 947, 967, 974, 996] [539, 581, 686, 821, 849, 856, 897, 906]
H_Z (250 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, 173] [7, 18, 19, 44, 48, 103, 113, 237] [8, 21, 22, 52, 56, 121, 131, 273] [3, 10, 26, 61, 64, 144, 149, 321] [4, 12, 31, 68, 74, 161, 174, 349] [13, 33, 34, 78, 82, 182, 192, 389] [5, 15, 38, 88, 91, 206, 211, 438] [6, 17, 42, 96, 99, 224, 229, 467] [19, 46, 47, 75, 107, 110, 178, 246] [20, 49, 50, 114, 118, 259, 268, 521] [22, 54, 55, 125, 128, 282, 289, 458] [23, 57, 58, 132, 136, 295, 304, 575] [9, 25, 62, 139, 145, 312, 322, 515] [10, 27, 66, 151, 154, 330, 333, 494] [11, 29, 69, 156, 162, 337, 350, 623] [30, 71, 72, 166, 170, 357, 367, 656] [12, 32, 76, 176, 179, 380, 384, 695] [34, 80, 81, 163, 186, 189, 354, 398] [35, 83, 84, 193, 197, 411, 420, 737] [14, 37, 89, 201, 207, 429, 439, 731] [15, 39, 93, 213, 216, 447, 450, 713] [16, 41, 97, 219, 225, 457, 468, 703] [17, 43, 101, 231, 234, 478, 482, 803] [18, 45, 105, 239, 242, 492, 497, 814] [27, 47, 109, 226, 250, 252, 471, 510] [48, 70, 111, 112, 165, 255, 515, 654] [50, 116, 117, 145, 175, 263, 393, 715] [51, 119, 120, 147, 180, 269, 537, 848] [21, 53, 123, 275, 278, 547, 551, 708] [37, 55, 90, 102, 127, 209, 286, 440] [56, 129, 130, 290, 293, 454, 568, 862] [58, 134, 135, 216, 299, 479, 580, 838] [28, 67, 137, 157, 307, 338, 481, 624] [24, 60, 140, 181, 308, 388, 578, 705] [61, 142, 143, 265, 314, 318, 445, 532] [25, 63, 135, 147, 281, 301, 323, 583] [26, 65, 152, 259, 289, 326, 522, 567] [68, 159, 160, 342, 346, 630, 639, 891] [29, 70, 164, 352, 355, 649, 652, 907] [72, 168, 169, 339, 361, 364, 628, 664] [73, 171, 172, 368, 372, 597, 673, 682] [31, 75, 177, 376, 381, 689, 696, 923] [32, 77, 128, 181, 288, 386, 566, 703] [33, 79, 184, 391, 394, 504, 711, 716] [39, 81, 146, 188, 325, 402, 404, 727] [82, 158, 190, 191, 341, 407, 731, 890] [84, 195, 196, 207, 351, 415, 547, 660] [85, 198, 199, 209, 356, 421, 565, 751] [36, 87, 112, 202, 257, 277, 425, 518] [88, 204, 205, 290, 417, 431, 435, 701] [38, 92, 113, 214, 258, 411, 443, 738] [40, 93, 95, 217, 220, 451, 452, 628] [96, 222, 223, 328, 430, 461, 465, 760] [41, 98, 227, 306, 469, 472, 589, 794] [42, 100, 232, 473, 479, 568, 646, 804] [43, 102, 236, 483, 485, 549, 690, 809] [44, 104, 240, 409, 488, 493, 735, 768] [45, 106, 244, 499, 502, 661, 817, 915] [46, 108, 213, 248, 445, 446, 504, 776] [110, 173, 221, 253, 254, 373, 374, 460] [49, 115, 261, 523, 525, 544, 838, 839] [100, 117, 233, 245, 265, 481, 531, 637] [118, 266, 267, 353, 533, 536, 650, 846] [120, 211, 271, 485, 539, 609, 818, 849] [94, 218, 272, 453, 541, 725, 819, 956] [52, 122, 276, 447, 543, 548, 778, 779] [53, 124, 280, 346, 553, 638, 856, 897] [54, 126, 284, 558, 560, 700, 734, 959] [87, 130, 203, 225, 241, 292, 399, 496] [92, 131, 215, 227, 294, 371, 679, 929] [57, 133, 297, 489, 577, 579, 715, 868] [136, 302, 303, 532, 586, 688, 707, 938] [137, 154, 305, 306, 587, 733, 836, 984] [59, 138, 309, 424, 591, 755, 871, 952] [139, 253, 310, 311, 340, 514, 596, 639] [60, 141, 247, 303, 506, 548, 585, 649] [143, 316, 317, 560, 588, 592, 808, 816] [144, 269, 319, 320, 348, 576, 605, 641] [62, 146, 324, 606, 607, 635, 811, 985] [63, 148, 162, 351, 366, 497, 647, 671] [64, 150, 272, 406, 570, 678, 740, 928] [127, 151, 287, 328, 329, 563, 611, 814] [65, 153, 196, 304, 397, 417, 550, 747] [66, 121, 155, 274, 334, 354, 544, 651] [156, 234, 335, 336, 517, 617, 880, 989] [67, 158, 340, 496, 626, 629, 858, 888] [160, 296, 344, 345, 578, 634, 637, 894] [161, 347, 348, 456, 640, 642, 762, 902] [69, 163, 319, 353, 602, 646, 856, 906] [71, 167, 359, 484, 658, 661, 723, 912] [77, 169, 208, 363, 442, 523, 666, 668] [133, 170, 298, 365, 366, 670, 851, 923] [172, 224, 370, 371, 381, 466, 625, 677] [74, 98, 175, 191, 228, 377, 409, 734] [114, 176, 260, 378, 379, 679, 690, 908] [76, 180, 192, 387, 410, 543, 673, 699] [78, 183, 392, 542, 671, 707, 712, 942] [79, 185, 396, 718, 721, 810, 893, 950] [80, 187, 386, 400, 701, 702, 723, 946] [141, 189, 313, 349, 405, 406, 643, 644] [83, 194, 220, 413, 458, 739, 741, 961] [197, 287, 418, 419, 564, 627, 750, 887] [199, 250, 384, 423, 535, 753, 774, 951] [86, 200, 426, 685, 756, 935, 969, 998] [201, 256, 297, 405, 427, 428, 517, 761] [205, 242, 300, 433, 434, 498, 513, 757] [206, 274, 421, 436, 437, 622, 770, 884] [89, 208, 441, 586, 771, 772, 793, 882] [90, 210, 280, 338, 555, 625, 716, 886] [91, 212, 262, 424, 669, 801, 899, 924] [164, 219, 356, 367, 455, 456, 655, 672] [95, 221, 380, 459, 562, 693, 694, 786] [223, 463, 464, 618, 783, 788, 921, 978] [97, 226, 362, 470, 665, 795, 885, 990] [99, 230, 254, 416, 474, 524, 746, 798] [231, 301, 476, 477, 533, 684, 801, 959] [101, 178, 235, 295, 383, 484, 576, 807] [103, 236, 238, 486, 489, 763, 810, 978] [142, 239, 315, 490, 491, 599, 697, 813] [104, 150, 241, 327, 419, 495, 712, 749] [105, 243, 500, 720, 818, 846, 939, 961] [106, 245, 503, 651, 692, 820, 909, 941] [107, 247, 292, 505, 571, 822, 823, 971] [108, 249, 372, 508, 680, 681, 827, 932] [109, 182, 251, 390, 483, 511, 708, 808] [188, 252, 357, 403, 467, 513, 657, 728] [111, 256, 326, 516, 609, 610, 752, 832] [202, 243, 347, 389, 501, 509, 706, 819] [165, 345, 382, 520, 636, 698, 739, 895] [214, 310, 448, 482, 593, 780, 820, 949] [140, 171, 237, 369, 487, 675, 837, 925] [115, 262, 413, 527, 606, 672, 742, 876] [116, 186, 264, 399, 529, 724, 843, 954] [230, 267, 283, 475, 493, 506, 535, 824] [138, 235, 268, 342, 495, 631, 892, 992] [119, 270, 425, 538, 633, 732, 748, 919] [275, 313, 476, 545, 546, 595, 698, 815] [122, 277, 336, 550, 619, 620, 853, 881] [123, 279, 376, 408, 687, 688, 733, 939] [124, 281, 431, 556, 763, 827, 857, 910] [125, 257, 283, 519, 559, 603, 834, 860] [126, 285, 379, 394, 692, 717, 730, 936] [129, 291, 569, 727, 807, 863, 974, 984] [203, 279, 364, 430, 554, 561, 623, 669] [177, 293, 382, 572, 573, 697, 866, 943] [149, 215, 449, 756, 799, 857, 926, 970] [273, 474, 507, 542, 785, 826, 830, 925] [132, 296, 330, 508, 613, 614, 693, 738] [134, 300, 444, 518, 582, 691, 788, 833] [307, 428, 459, 488, 590, 759, 760, 811] [294, 308, 360, 516, 534, 574, 721, 867] [311, 337, 594, 595, 621, 622, 834, 885] [312, 453, 597, 783, 802, 817, 905, 938] [148, 317, 331, 373, 463, 683, 789, 933] [318, 422, 566, 601, 659, 765, 853, 985] [320, 603, 604, 607, 711, 872, 874, 889] [321, 363, 404, 505, 630, 667, 730, 921] [260, 323, 407, 524, 572, 782, 875, 903] [329, 446, 477, 540, 612, 702, 754, 777] [152, 331, 455, 615, 638, 784, 812, 979] [153, 229, 332, 591, 743, 872, 937, 964] [155, 200, 420, 604, 617, 714, 875, 982] [157, 339, 436, 478, 522, 627, 767, 802] [159, 334, 343, 462, 616, 632, 855, 893] [193, 244, 352, 412, 471, 537, 648, 796] [166, 218, 358, 454, 555, 659, 824, 913] [167, 360, 511, 663, 829, 841, 916, 919] [168, 332, 362, 612, 616, 654, 865, 908] [374, 402, 652, 684, 749, 934, 944, 997] [174, 375, 539, 686, 850, 904, 986, 995] [179, 385, 414, 531, 611, 685, 845, 878] [204, 391, 432, 470, 536, 709, 710, 764] [183, 212, 393, 444, 681, 714, 913, 931] [184, 395, 564, 719, 804, 837, 918, 951] [185, 397, 452, 502, 722, 782, 831, 953] [187, 276, 401, 549, 642, 813, 900, 901] [190, 408, 443, 732, 774, 775, 933, 958] [377, 395, 621, 656, 720, 726, 910, 952] [341, 461, 487, 620, 650, 736, 842, 883] [333, 387, 427, 704, 758, 947, 953, 996] [194, 414, 582, 596, 675, 743, 771, 974] [195, 263, 361, 416, 528, 745, 844, 965] [198, 228, 422, 464, 480, 752, 806, 930] [309, 429, 592, 613, 762, 835, 862, 950] [210, 316, 434, 448, 600, 643, 903, 994] [255, 435, 469, 683, 766, 793, 892, 941] [437, 768, 769, 772, 869, 912, 970, 972] [438, 499, 636, 668, 724, 816, 880, 896] [266, 412, 440, 534, 670, 740, 847, 973] [217, 375, 587, 682, 769, 874, 914, 973] [457, 686, 737, 759, 785, 906, 936, 957] [222, 441, 462, 558, 648, 787, 859, 932] [270, 392, 465, 600, 713, 790, 894, 990] [466, 492, 631, 653, 791, 795, 955, 982] [288, 473, 514, 538, 799, 800, 831, 968] [232, 365, 480, 699, 805, 944, 945, 994] [233, 400, 527, 551, 725, 758, 842, 955] [238, 403, 605, 729, 794, 845, 884, 977] [325, 368, 396, 491, 608, 626, 674, 751] [240, 494, 574, 664, 789, 815, 900, 976] [246, 418, 503, 674, 748, 821, 897, 924] [248, 507, 554, 593, 825, 864, 868, 895] [249, 359, 509, 567, 662, 828, 917, 997] [251, 512, 557, 641, 677, 879, 881, 899] [442, 460, 577, 640, 663, 710, 773, 898] [498, 520, 528, 695, 718, 823, 836, 883] [258, 401, 569, 584, 632, 726, 798, 980] [261, 291, 410, 526, 570, 665, 864, 920] [264, 278, 530, 552, 565, 766, 854, 917] [315, 335, 451, 475, 526, 618, 781, 841] [426, 521, 594, 689, 757, 778, 829, 960] [271, 540, 608, 619, 746, 851, 882, 948] [439, 541, 599, 729, 800, 822, 852, 983] [343, 546, 633, 728, 806, 957, 963, 993] [423, 553, 589, 754, 773, 833, 866, 928] [282, 556, 557, 598, 844, 858, 915, 993] [284, 369, 501, 676, 761, 839, 926, 943] [285, 383, 433, 561, 704, 765, 847, 979] [286, 562, 585, 657, 870, 873, 896, 975] [552, 573, 581, 694, 849, 855, 860, 942] [298, 314, 472, 598, 706, 797, 887, 964] [299, 388, 581, 645, 791, 821, 902, 972] [302, 510, 584, 828, 876, 886, 986, 989] [575, 735, 741, 854, 861, 960, 962, 983] [305, 327, 432, 588, 705, 742, 948, 963] [322, 512, 787, 830, 947, 975, 981, 999] [390, 583, 667, 770, 786, 877, 922, 966] [324, 378, 545, 658, 691, 750, 911, 940] [529, 610, 696, 755, 764, 826, 922, 968] [563, 644, 666, 784, 861, 888, 931, 980] [490, 614, 805, 812, 843, 879, 969, 988] [344, 449, 530, 635, 777, 781, 796, 890] [350, 645, 753, 863, 905, 967, 988, 991] [355, 653, 676, 747, 776, 904, 966, 976] [358, 385, 660, 700, 825, 901, 914, 992] [590, 647, 662, 809, 891, 918, 920, 998] [450, 655, 687, 852, 867, 909, 937, 981] [370, 415, 486, 634, 678, 744, 792, 927] [398, 559, 680, 722, 803, 878, 898, 930] [580, 717, 736, 744, 797, 907, 916, 954] [602, 745, 775, 832, 873, 935, 940, 956] [615, 709, 779, 840, 850, 949, 965, 977] [468, 780, 792, 877, 911, 962, 967, 996] [767, 859, 871, 927, 945, 958, 971, 995] [500, 629, 790, 870, 889, 929, 946, 991] [519, 525, 624, 835, 840, 934, 987, 999] [571, 579, 601, 719, 848, 865, 869, 987]
Code ID 1000-502-6 · download JSON · raw on GitHub