[[720,74,8]] · QEC Challenge

[[720,74,8]] d =

720

kd²/n

6.57778

X/Z

Share this result

Distance

X/Z asymmetry 1 · d_X = 8, d_Z = 8 · w_X = 5, w_Z = 4 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)

d_X 8 · witness weight 8 (claimed exact)

witness operator (support, 8 qubits)

[0, 1, 3, 20, 32, 36, 57, 162]

d_Z 8 · witness weight 8 (claimed exact)

witness operator (support, 8 qubits)

[0, 1, 3, 20, 32, 36, 93, 153]

certificate exact, d = 8 · 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 < 8 exists; Z: no logical < 8 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 10 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)

check weights H_X 5 · H_Z 4

qubit degrees H_X 2 · H_Z 2

trapping sets H_X (1,2)×720 (2,2)×2880 (3,2)×11520 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,2): 720 (2,2): 2880 (3,2): 11520 (3,4): 2880

trapping sets H_Z (1,2)×720 (2,2)×2160 (3,2)×6480 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

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

(1,2): 720 (2,2): 2160 (3,2): 6480 (3,4): 1440

Construction & provenance

authors @TimoKellerMath

provenance submitted through the challenge

novelty new parameter set claimed by submitter

construction Two-sheeted cyclic cover of the {4,5} surface code [[360,38,8]] of the orientably-regular map R19.3 (M. Conder's list of reflexible maps of genus 2 to 301, genus 19; the board entry 360-38-8 is this base code). Base group G = <r,s | r⁴, s⁵, (r*s)², s*r^-2*s²*r*s^-1*r²*s^-1*r*s*r^-1*s^-1*r*s> of order 720; darts = elements of G (right multiplication), faces g<r>, vertices g<s>, edges g<rs> = {g, grs}. Voltage omega in Z/2 on the base edges, equal to 1 exactly on the 41 edges {w, w*r*s} for w in: r^-1*s^-1; s*r^-1; s^-2; r^-1*s^-2; s^-2*r; r*s^-2*r*s^-1; r^-1*s*r^-1*s^-1*r; s^-2*r*s^-1*r; r²*s^-2*r*s^-1; r*s*r^-1*s^-1*r*s^-1; r*s²*r^-1*s*r^-1; s*r^-1*s^-1*r*s^-2; s^-1*r*s^-2*r*s^-1; r²*s²*r^-1*s*r^-1; r*s*r^-1*s*r^-1*s^-2; r*s^-1*r*s*r^-1*s*r^-1; r^-1*s*r^-1*s^-1*r*s^-1*r; s^-2*r*s^-1*r*s^-1*r; r²*s*r^-1*s^-1*r*s^-1*r; r²*s^-1*r*s*r^-1*s*r^-1; r²*s^-1*r*s*r^-1*s^-2; r²*s^-1*r*s^-1*r*s^-2; r*s*r^-1*s^-1*r*s^-2*r; r^-1*s*r^-1*s^-1*r*s^-1*r*s^-1; s*r^-1*s^-1*r*s^-1*r*s*r^-1; s^-1*r*s²*r^-1*s*r^-1*s^-1; s^-1*r*s^-1*r*s*r^-1*s*r^-1; s^-1*r*s^-1*r*s*r^-1*s^-2; r²*s*r^-1*s*r^-1*s^-1*r*s^-1; r²*s*r^-1*s²*r^-1*s*r^-1; r²*s*r^-1*s^-1*r*s^-1*r*s^-1; r*s*r^-1*s*r^-1*s*r^-1*s^-1*r; r*s^-1*r*s^-1*r*s^-2*r*s^-1; r^-1*s*r^-1*s*r^-1*s^-2*r*s^-1; r^-1*s^-1*r*s*r^-1*s*r^-1*s^-2; s*r^-1*s*r^-1*s^-2*r*s^-1*r; r²*s^-1*r*s^-1*r*s^-1*r*s*r^-1; r²*s^-1*r*s^-1*r*s^-1*r*s^-2; r*s*r^-1*s*r^-1*s*r^-1*s^-1*r*s^-1; r*s²*r^-1*s*r^-1*s^-2*r*s^-1; r^-1*s^-1*r*s*r^-1*s*r^-1*s*r^-1*s^-1. Cover darts (g,i), g in G, i in Z/2, with R~(g,i) = (g r, i + omega(g)) and S~(g,i) = (g s, i), omega(g) the voltage of the edge through g; faces, vertices and edges are the cycles of R~, S~ and R~S~: (V,E,F) = (288,720,360), genus 37. Qubits on the 720 edges, X-checks on the 288 vertices (weight 5), Z-checks on the 360 faces (weight 4), incidences mod 2, so k = 2 - chi = 74. Not a regular map (no orientably-regular {4,5} map of genus 37 exists). The qubit order is that of the public package in the references (data/maps.json: base darts and a cohomologous voltage with 87 edges), whose src/rebuild.py rebuilds these matrices and checks the isomorphism with the cover above.

model Claude Opus 5.5 (claimed, not verified)

builds on https://arxiv.org/abs/1506.04029, https://www.math.auckland.ac.nz/~conder/RegularOrientableMaps301.txt, https://github.com/TimoKellerMath/quantum-error-correction/tree/2e97a5361e7b9327128baa242bdedd333f7d7e12/hyperbolic-map-codes

date 2026-11-10

notes Exact distance d_X = d_Z = 8: tropidist (arXiv:2611.08247) at the board's pinned commit b03ec2d4077f closes both sides (certs/720-74-8.json, level solver); independently two exact programs for check matrices with column weight 2 and an enumeration of all circuits of length <= 8 (100 X-type and 6108 Z-type logical operators of weight 8, 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 ≤ 6 (computed)

How this code was found

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

[[720,74,8]]: double cover of the {4,5} surface code of the map R19.3

Direction & hypothesis

Cell: check weight at most 6 (here 5 and 4), unrestricted locality (no layout submitted). The {4,5} surface codes of regular maps reach d = 8 at [[360,38,8]], but the next {4,5} maps of the census with d >= 8 are [[660,68,8]], [[960,98,8]] and [[1280,130,8]], so there are large gaps in n. A two-sheeted cyclic cover doubles V, E and F, so k = 2 - 2 chi_0 = 2 k_0 - 2 for the base's chi_0 and k_0 = 38. A shortest nontrivial cycle of the base graph with voltage 0 lifts to a nontrivial cycle of the same length (the projection maps boundaries to boundaries), while a nontrivial cycle of the cover may project to a trivial one, so a double cover can lose distance. Hypothesis: for suitable voltages it keeps d = 8, and double covers of [[360,38,8]] give [[720,74,8]] at check weight 5.

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 a double cover of the {4,5} map R19.3 (voltage in the construction of the entry). All ten sampled double covers of R19.3 (inequivalent voltage classes up to the automorphisms of the base map) are [[720,74,8]]; 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 = 74 = 720 - 287 - 359 (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 8, 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 8 with a row-space test: the graph of the map has girth 4: its 360 circuits of length 4 and 720 of length 6 are all trivial, 6108 of the 8268 circuits of length 8 are nontrivial (Z-type logical operators of weight 8); the dual graph has 288 circuits of length 5, all trivial, and 100 of its 820 circuits of length 8 are nontrivial; (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 8 and 8 in 1.9 s and 1.8 s, recorded in certs/720-74-8.json.
Final claim: d_X = d_Z = 8, exact (computer-assisted; the four computations agree). 100 X-type and 6108 Z-type logical operators have weight 8.

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).
Of the 321 cyclic covers of {4,5} maps in the census (n <= 1000), only the ten double covers of R19.3 reach d = 8; the others have d <= 6.
Random cyclic covers rarely raise the distance: 122 of the 2000 covers have a larger d than their base, 1827 keep both side distances of the base.

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^4, s^5, (r*s)^2, s*r^-2*s^2*r*s^-1*r^2*s^-1*r*s*r^-1*s^-1*r*s> (order 720, the base map R19.3); the 41 voltage words are in the construction of the entry and in hyperbolic-map-codes/data/cover_voltage.txt; 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 288 (max weight 5) · Z-checks 360 (max weight 4)

H_X (288 checks, sparse supports)

[0, 2, 3, 7, 9] [0, 1, 5, 11, 13] [2, 4, 6, 15, 17] [1, 4, 10, 20, 22] [7, 14, 16, 29, 30] [3, 8, 18, 32, 34] [8, 11, 23, 40, 41] [5, 12, 24, 42, 44] [6, 14, 26, 46, 48] [9, 19, 28, 35, 52] [17, 21, 31, 55, 56] [12, 20, 36, 62, 63] [10, 21, 37, 64, 66] [13, 25, 39, 45, 70] [15, 27, 49, 54, 80] [16, 28, 50, 81, 83] [30, 47, 53, 87, 88] [19, 32, 57, 93, 94] [18, 33, 58, 95, 97] [22, 38, 61, 67, 102] [23, 39, 68, 108, 110] [33, 41, 71, 114, 115] [25, 42, 72, 117, 118] [24, 43, 73, 119, 121] [27, 46, 76, 125, 127] [26, 47, 77, 128, 130] [29, 51, 84, 86, 138] [52, 82, 85, 140, 141] [31, 54, 89, 145, 147] [56, 65, 91, 150, 151] [34, 59, 92, 98, 154] [35, 60, 99, 139, 161] [36, 61, 100, 153, 162] [43, 63, 103, 167, 168] [38, 64, 104, 170, 172] [37, 65, 105, 173, 175] [40, 69, 111, 113, 182] [70, 109, 112, 184, 185] [44, 74, 116, 122, 190] [45, 75, 123, 183, 197] [48, 78, 126, 131, 199] [49, 79, 132, 206, 208] [51, 81, 134, 169, 211] [50, 82, 135, 187, 212] [53, 86, 142, 219, 222] [88, 129, 144, 225, 227] [55, 90, 148, 149, 231] [80, 133, 146, 209, 232] [57, 92, 101, 152, 162] [60, 94, 155, 240, 242] [59, 95, 156, 244, 246] [58, 96, 157, 247, 250] [62, 101, 164, 166, 257] [102, 163, 165, 254, 259] [66, 106, 171, 176, 263] [67, 107, 177, 258, 270] [69, 108, 124, 178, 198] [68, 109, 179, 271, 274] [71, 113, 136, 186, 212] [96, 115, 188, 283, 284] [72, 90, 116, 145, 189] [75, 118, 191, 243, 288] [74, 119, 192, 290, 292] [73, 120, 193, 294, 296] [79, 127, 200, 304, 305] [78, 128, 202, 239, 307] [77, 129, 203, 308, 311] [83, 136, 210, 214, 290] [84, 137, 215, 319, 322] [85, 139, 217, 324, 326] [141, 177, 213, 269, 328] [87, 143, 223, 226, 333] [138, 216, 221, 323, 334] [89, 146, 220, 228, 329] [91, 149, 233, 237, 342] [151, 174, 235, 321, 347] [93, 153, 237, 241, 350] [154, 194, 236, 238, 294] [97, 158, 245, 251, 354] [98, 159, 252, 351, 361] [99, 160, 253, 259, 363] [100, 163, 234, 255, 342] [103, 166, 260, 272, 368] [120, 168, 262, 371, 372] [107, 172, 264, 289, 375] [106, 173, 265, 303, 377] [105, 174, 266, 379, 382] [110, 180, 201, 275, 303] [111, 181, 224, 276, 336] [112, 183, 278, 318, 391] [132, 185, 207, 273, 314] [114, 187, 281, 282, 395] [182, 277, 280, 320, 388] [117, 147, 229, 287, 331] [190, 285, 286, 360, 380] [121, 194, 291, 297, 403] [122, 195, 298, 401, 408] [123, 196, 232, 299, 341] [199, 248, 301, 302, 357] [130, 204, 306, 312, 415] [131, 205, 238, 351, 412] [133, 206, 313, 352, 417] [137, 211, 316, 419, 420] [135, 213, 317, 394, 421] [140, 218, 270, 327, 424] [161, 254, 325, 364, 425] [142, 218, 221, 324, 330] [227, 253, 338, 362, 381] [148, 230, 262, 335, 370] [150, 234, 344, 346, 393] [231, 340, 345, 422, 431] [152, 236, 256, 349, 397] [160, 242, 353, 400, 432] [159, 217, 246, 325, 383] [249, 295, 328, 358, 373] [164, 188, 256, 282, 396] [165, 258, 366, 386, 413] [167, 261, 369, 370, 437] [257, 365, 367, 387, 435] [263, 298, 309, 374, 407] [175, 267, 376, 383, 439] [176, 268, 384, 408, 411] [181, 198, 300, 410, 440] [179, 273, 385, 420, 436] [184, 208, 279, 392, 416] [197, 209, 315, 390, 418] [186, 280, 389, 393, 441] [284, 310, 398, 399, 409] [189, 230, 285, 400, 444] [196, 288, 311, 402, 419] [278, 293, 312, 390, 404] [295, 314, 348, 381, 406] [207, 305, 405, 414, 446] [205, 297, 307, 313, 416] [223, 332, 425, 427, 439] [225, 255, 337, 363, 428] [260, 333, 364, 367, 386] [283, 332, 339, 397, 426] [315, 343, 395, 417, 429] [327, 355, 402, 423, 436] [269, 356, 375, 434, 438] [359, 366, 378, 424, 433] [281, 394, 415, 418, 443] [392, 403, 430, 442, 445] [447, 449, 450, 454, 456] [447, 448, 452, 458, 460] [449, 451, 453, 462, 464] [448, 451, 457, 467, 469] [454, 461, 463, 476, 477] [450, 455, 465, 479, 481] [455, 458, 470, 487, 488] [452, 459, 471, 489, 491] [453, 461, 473, 493, 495] [456, 466, 475, 482, 499] [464, 468, 478, 502, 503] [459, 467, 483, 509, 510] [457, 468, 484, 511, 513] [460, 472, 486, 492, 517] [462, 474, 496, 501, 526] [463, 475, 497, 527, 529] [477, 494, 500, 533, 534] [466, 479, 504, 539, 540] [465, 480, 505, 541, 543] [469, 485, 508, 514, 548] [470, 486, 515, 553, 555] [480, 488, 518, 559, 560] [472, 489, 519, 562, 563] [471, 490, 520, 564, 566] [178, 201, 474, 493, 569] [473, 494, 523, 570, 572] [476, 498, 530, 532, 579] [499, 528, 531, 581, 582] [478, 501, 535, 584, 586] [503, 512, 537, 589, 590] [481, 506, 538, 544, 593] [482, 507, 545, 580, 596] [483, 508, 546, 592, 597] [490, 510, 549, 602, 603] [134, 210, 485, 511, 604] [484, 512, 550, 605, 607] [487, 516, 556, 558, 612] [517, 554, 557, 614, 615] [491, 521, 561, 567, 620] [492, 522, 568, 613, 623] [124, 495, 524, 573, 625] [496, 525, 574, 627, 629] [104, 171, 498, 527, 631] [497, 528, 576, 617, 632] [220, 229, 500, 532, 583] [276, 534, 571, 638, 639] [502, 536, 587, 588, 641] [526, 575, 585, 630, 642] [504, 538, 547, 591, 597] [202, 306, 507, 540, 647] [191, 287, 506, 541, 648] [248, 356, 358, 505, 542] [509, 547, 599, 601, 653] [548, 598, 600, 650, 655] [169, 513, 551, 608, 658] [514, 552, 609, 654, 660] [76, 126, 516, 553, 624] [261, 272, 515, 554, 610] [518, 558, 577, 616, 632] [542, 560, 618, 666, 667] [519, 536, 561, 584, 619] [156, 245, 522, 563, 669] [264, 293, 521, 564, 670] [405, 406, 520, 565, 671] [265, 376, 525, 569, 676] [155, 241, 524, 570, 677] [309, 409, 523, 571, 678] [170, 391, 529, 577, 670] [235, 320, 346, 530, 578] [331, 531, 580, 634, 683] [582, 609, 633, 659, 686] [224, 329, 533, 637, 688] [335, 340, 388, 579, 636] [143, 219, 426, 535, 585] [429, 537, 588, 645, 689] [215, 348, 385, 590, 606] [239, 352, 539, 592, 645] [593, 621, 644, 646, 671] [243, 355, 357, 433, 543] [286, 401, 544, 594, 690] [545, 595, 649, 655, 691] [546, 598, 643, 651, 689] [180, 271, 549, 601, 656] [317, 373, 565, 603, 657] [192, 291, 552, 604, 696] [200, 378, 551, 605, 675] [362, 380, 432, 550, 606] [125, 368, 413, 555, 675] [144, 226, 387, 556, 611] [214, 389, 557, 613, 662] [574, 615, 628, 661, 681] [559, 617, 664, 665, 704] [216, 319, 435, 612, 663] [222, 244, 326, 562, 586] [252, 267, 379, 620, 668] [289, 566, 621, 673, 708] [361, 404, 567, 674, 709] [339, 398, 568, 622, 642] [158, 247, 300, 384, 625] [240, 407, 572, 679, 710] [411, 573, 626, 646, 690] [350, 575, 627, 680, 712] [374, 578, 631, 714, 715] [371, 444, 576, 633, 703] [581, 635, 660, 685, 716] [596, 650, 684, 692, 717] [437, 583, 635, 636, 683] [266, 310, 639, 649, 697] [334, 587, 640, 657, 695] [322, 442, 589, 643, 702] [323, 343, 365, 396, 641] [446, 591, 644, 652, 705] [382, 443, 595, 647, 706] [594, 634, 648, 684, 698] [157, 372, 399, 672, 686] [431, 599, 618, 652, 665] [275, 600, 654, 693, 699] [274, 330, 423, 602, 695] [277, 336, 422, 653, 694] [204, 308, 316, 658, 674] [304, 360, 607, 698, 719] [301, 359, 412, 608, 709] [302, 337, 434, 611, 624] [321, 610, 661, 715, 718] [441, 614, 629, 701, 711] [623, 630, 682, 700, 713] [279, 318, 616, 663, 702] [203, 249, 299, 338, 667] [421, 619, 640, 668, 706] [622, 669, 678, 707, 714] [195, 292, 662, 679, 700] [193, 347, 672, 681, 697] [296, 349, 427, 628, 676] [626, 673, 677, 680, 711] [414, 637, 687, 717, 719] [430, 440, 638, 651, 691] [656, 688, 692, 694, 699] [228, 341, 666, 687, 705] [233, 345, 682, 704, 712] [354, 369, 685, 707, 718] [250, 410, 445, 659, 696] [251, 268, 377, 693, 716] [353, 664, 703, 710, 713] [344, 428, 438, 701, 708]

H_Z (360 checks, sparse supports)

[0, 1, 2, 4] [2, 6, 7, 14] [0, 3, 8, 11] [1, 5, 12, 20] [7, 9, 16, 28] [4, 10, 17, 21] [3, 9, 19, 32] [11, 13, 23, 39] [5, 13, 25, 42] [6, 15, 27, 46] [14, 26, 30, 47] [15, 17, 31, 54] [8, 18, 33, 41] [20, 22, 36, 61] [10, 22, 38, 64] [12, 24, 43, 63] [16, 29, 51, 81] [28, 50, 52, 82] [29, 30, 53, 86] [21, 37, 56, 65] [32, 34, 57, 92] [18, 34, 59, 95] [19, 35, 60, 94] [23, 40, 69, 108] [39, 68, 70, 109] [40, 41, 71, 113] [42, 44, 72, 116] [24, 44, 74, 119] [25, 45, 75, 118] [46, 48, 76, 126] [26, 48, 78, 128] [27, 49, 79, 127] [35, 52, 85, 139] [47, 77, 88, 129] [31, 55, 90, 145] [54, 80, 89, 146] [55, 56, 91, 149] [33, 58, 96, 115] [36, 62, 101, 162] [61, 100, 102, 163] [62, 63, 103, 166] [64, 66, 104, 171] [37, 66, 106, 173] [38, 67, 107, 172] [45, 70, 112, 183] [43, 73, 120, 168] [49, 80, 133, 206] [81, 83, 134, 210] [50, 83, 136, 212] [51, 84, 137, 211] [82, 135, 141, 213] [53, 87, 143, 219] [86, 138, 142, 221] [87, 88, 144, 226] [65, 105, 151, 174] [57, 93, 153, 162] [92, 152, 154, 236] [93, 94, 155, 241] [95, 97, 156, 245] [58, 97, 158, 247] [59, 98, 159, 246] [60, 99, 160, 242] [67, 102, 165, 258] [108, 110, 178, 201] [68, 110, 180, 271] [69, 111, 181, 198] [109, 179, 185, 273] [71, 114, 187, 212] [113, 182, 186, 280] [114, 115, 188, 282] [72, 117, 145, 147] [116, 189, 190, 285] [117, 118, 191, 287] [119, 121, 192, 291] [73, 121, 194, 294] [74, 122, 195, 292] [75, 123, 196, 288] [124, 178, 493, 495] [76, 125, 553, 555] [126, 199, 302, 624] [125, 127, 200, 675] [128, 130, 202, 306] [77, 130, 204, 308] [78, 131, 205, 307] [79, 132, 207, 305] [84, 138, 216, 319] [85, 140, 218, 324] [139, 161, 217, 325] [140, 141, 177, 270] [129, 203, 227, 338] [89, 147, 220, 229] [90, 148, 189, 230] [146, 228, 232, 341] [91, 150, 234, 342] [149, 231, 233, 345] [150, 151, 235, 346] [98, 154, 238, 351] [96, 157, 284, 399] [99, 161, 254, 259] [100, 153, 237, 342] [101, 152, 164, 256] [163, 255, 259, 363] [103, 167, 261, 272] [166, 257, 260, 367] [167, 168, 262, 370] [134, 169, 511, 513] [104, 170, 527, 529] [171, 263, 374, 631] [170, 172, 264, 670] [173, 175, 265, 376] [105, 175, 267, 379] [106, 176, 268, 377] [107, 177, 269, 375] [111, 182, 277, 336] [112, 184, 279, 318] [183, 197, 278, 390] [132, 184, 185, 208] [122, 190, 286, 401] [120, 193, 372, 672] [123, 197, 209, 232] [124, 198, 300, 625] [131, 199, 301, 412] [201, 265, 303, 569] [206, 208, 313, 416] [133, 209, 315, 417] [192, 210, 290, 604] [169, 211, 316, 658] [135, 187, 281, 394] [136, 186, 214, 389] [137, 215, 385, 420] [213, 317, 328, 373] [219, 222, 535, 586] [220, 329, 500, 533] [142, 222, 324, 326] [143, 223, 332, 426] [221, 330, 334, 695] [224, 276, 533, 534] [144, 225, 337, 611] [226, 333, 367, 387] [225, 227, 253, 363] [148, 231, 335, 340] [174, 266, 347, 697] [236, 294, 296, 349] [202, 239, 539, 540] [155, 240, 570, 572] [241, 350, 677, 680] [240, 242, 353, 710] [191, 243, 541, 543] [156, 244, 562, 563] [245, 354, 669, 707] [217, 244, 246, 326] [247, 250, 300, 410] [248, 357, 505, 543] [249, 358, 542, 667] [157, 250, 659, 686] [158, 251, 268, 384] [159, 252, 267, 383] [160, 253, 362, 432] [164, 257, 365, 396] [165, 254, 364, 386] [258, 270, 366, 424] [176, 263, 298, 408] [271, 274, 549, 602] [272, 368, 515, 555] [179, 274, 423, 436] [180, 275, 656, 699] [181, 276, 440, 638] [273, 314, 348, 385] [280, 320, 346, 393] [188, 256, 283, 397] [282, 343, 395, 396] [283, 284, 339, 398] [285, 380, 400, 432] [287, 331, 634, 648] [243, 288, 355, 402] [264, 289, 564, 566] [291, 403, 445, 696] [214, 290, 292, 662] [293, 404, 521, 567] [295, 373, 406, 565] [193, 296, 628, 681] [194, 205, 238, 297] [195, 298, 407, 679] [196, 203, 299, 311] [248, 302, 356, 434] [200, 304, 605, 607] [275, 303, 377, 693] [304, 305, 414, 719] [306, 415, 443, 647] [239, 307, 313, 352] [308, 311, 316, 419] [309, 407, 523, 572] [310, 409, 571, 639] [204, 312, 404, 674] [207, 314, 405, 406] [318, 391, 577, 616] [319, 322, 663, 702] [320, 388, 530, 579] [235, 321, 578, 715] [215, 322, 589, 590] [216, 323, 365, 435] [218, 327, 330, 423] [325, 383, 425, 439] [269, 328, 356, 358] [228, 329, 637, 687] [229, 331, 583, 683] [223, 333, 364, 425] [323, 334, 587, 641] [335, 370, 437, 636] [224, 336, 688, 694] [249, 295, 338, 381] [339, 426, 585, 642] [230, 262, 371, 444] [299, 341, 666, 667] [343, 429, 588, 641] [233, 237, 350, 712] [234, 255, 344, 428] [345, 431, 665, 704] [321, 347, 661, 681] [348, 362, 381, 606] [351, 361, 412, 709] [251, 354, 685, 716] [301, 357, 359, 433] [286, 360, 594, 698] [252, 361, 567, 620] [260, 368, 386, 413] [261, 369, 610, 718] [371, 372, 633, 686] [309, 374, 678, 714] [289, 375, 438, 708] [376, 427, 439, 676] [359, 378, 551, 608] [379, 382, 668, 706] [360, 380, 550, 607] [266, 382, 595, 649] [387, 435, 556, 612] [277, 340, 388, 422] [389, 441, 557, 614] [278, 293, 391, 670] [279, 392, 442, 702] [312, 390, 415, 418] [281, 315, 395, 418] [310, 399, 672, 697] [401, 408, 411, 690] [297, 392, 403, 416] [405, 446, 644, 671] [398, 409, 622, 678] [384, 411, 573, 625] [366, 378, 413, 675] [352, 417, 429, 645] [402, 419, 420, 436] [394, 421, 443, 706] [317, 421, 640, 657] [327, 355, 424, 433] [332, 349, 397, 427] [337, 428, 434, 438] [430, 442, 643, 651] [344, 393, 441, 701] [422, 431, 599, 653] [353, 400, 444, 703] [369, 437, 635, 685] [410, 430, 440, 445] [414, 446, 687, 705] [447, 448, 449, 451] [449, 453, 454, 461] [447, 450, 455, 458] [448, 452, 459, 467] [454, 456, 463, 475] [451, 457, 464, 468] [450, 456, 466, 479] [458, 460, 470, 486] [452, 460, 472, 489] [453, 462, 474, 493] [461, 473, 477, 494] [462, 464, 478, 501] [455, 465, 480, 488] [467, 469, 483, 508] [457, 469, 485, 511] [459, 471, 490, 510] [463, 476, 498, 527] [475, 497, 499, 528] [476, 477, 500, 532] [468, 484, 503, 512] [479, 481, 504, 538] [465, 481, 506, 541] [466, 482, 507, 540] [470, 487, 516, 553] [486, 515, 517, 554] [487, 488, 518, 558] [489, 491, 519, 561] [471, 491, 521, 564] [472, 492, 522, 563] [473, 495, 524, 570] [474, 496, 525, 569] [482, 499, 531, 580] [494, 523, 534, 571] [478, 502, 536, 584] [501, 526, 535, 585] [502, 503, 537, 588] [480, 505, 542, 560] [483, 509, 547, 597] [508, 546, 548, 598] [509, 510, 549, 601] [484, 513, 551, 605] [485, 514, 552, 604] [492, 517, 557, 613] [490, 520, 565, 603] [496, 526, 575, 627] [497, 529, 577, 632] [498, 530, 578, 631] [528, 576, 582, 633] [532, 579, 583, 636] [512, 550, 590, 606] [504, 539, 592, 597] [538, 591, 593, 644] [506, 544, 594, 648] [507, 545, 595, 647] [514, 548, 600, 654] [516, 556, 611, 624] [554, 610, 615, 661] [518, 559, 617, 632] [558, 612, 616, 663] [559, 560, 618, 665] [519, 562, 584, 586] [561, 619, 620, 668] [520, 566, 621, 671] [522, 568, 622, 669] [524, 573, 626, 677] [525, 574, 628, 676] [531, 581, 635, 683] [580, 596, 634, 684] [581, 582, 609, 660] [536, 587, 619, 640] [537, 589, 643, 689] [544, 593, 646, 690] [545, 596, 650, 655] [546, 592, 645, 689] [547, 591, 599, 652] [598, 651, 655, 691] [601, 653, 656, 694] [602, 603, 657, 695] [552, 609, 659, 696] [613, 623, 662, 700] [574, 614, 615, 629] [568, 623, 630, 642] [627, 629, 680, 711] [575, 630, 682, 712] [576, 617, 664, 703] [638, 639, 649, 691] [600, 650, 692, 699] [654, 660, 693, 716] [608, 658, 674, 709] [618, 652, 666, 705] [621, 626, 646, 673] [684, 698, 717, 719] [637, 688, 692, 717] [679, 700, 710, 713] [664, 682, 704, 713] [673, 701, 708, 711] [707, 714, 715, 718]

Code ID 720-74-8 · download JSON · raw on GitHub