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[[660,18,30]] d ≤
n
660
k
18
d
30
kd²/n
24.545
w
8
X/Z
1.5

Share this result

Distance

X/Z asymmetry 1.5 · d_X ≤ 45, d_Z ≤ 30 · 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 45 · witness weight 45 (claimed upper_bound)
witness found by @vprusso · verify/ris_gpu.py recover mode, pair depth 0 (GPU RIS, CPU re-verified) · found at 3×108 trials · survived 3×108 trials · 2026-09-25
witness operator (support, 45 qubits)
[0, 5, 10, 32, 37, 42, 48, 53, 58, 63, 68, 73, 91, 96, 101, 122, 127, 132, 139, 144, 149, 154, 159, 164, 183, 188, 193, 196, 201, 206, 214, 219, 224, 227, 232, 237, 241, 246, 251, 255, 260, 265, 300, 305, 310]
d_Z 30 · witness weight 30 (claimed upper_bound)
witness operator (support, 30 qubits)
[12, 33, 66, 67, 82, 83, 95, 105, 118, 152, 153, 177, 198, 231, 232, 247, 248, 260, 270, 283, 317, 318, 336, 345, 414, 426, 501, 510, 579, 591]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

Diagnostics

computed by the verifier from the parity checks, the layout, and the stored witnesses; shown as evidence, not used for ranking
girth H_X 4 · H_Z 4 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 8 · H_Z 8
qubit degrees H_X 4 · H_Z 4
trapping sets H_X (1,4)×660 (2,4)×330 (3,4)×60 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,4): 660 (2,4): 330 (2,6): 8580 (3,4): 60 (3,6): 9894 (3,8): 167898 (3,10): 14850
trapping sets H_Z (1,4)×660 (2,4)×330 (3,4)×60 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,4): 660 (2,4): 330 (2,6): 8580 (3,4): 60 (3,6): 9894 (3,8): 167898 (3,10): 14850

Construction & provenance

authors @edoaltamura
provenance submitted through the challenge
novelty novelty not audited
construction Generalized bicycle / regular lifted product over the metacyclic group C_22 semidirect C_15 with action r=5: H_X=[L(a)|R(b)], H_Z=[R(b)^T|L(a)^T], a=[18,142,163,293], b=[73,147,201,215], following arXiv:2306.16400.
model GPT-5 (claimed, not verified)
builds on arXiv:2306.16400
date 2026-08-28
notes Metacyclic 2BGA search. Screening archive: 1,200 random support mutations at 120 RIS trials; independent RIS checks at 1M, 2M, and 5M trials settled at d<=30 by 2M and held at 5M. Upper-bound confidence. Checked against the current board: no exact fingerprint or WL-equivalent entry; literature novelty remains unverified.
family generalized bicycle (a tag, not a ranking)
locality unrestricted (computed from the layout)
weight class weight ≤ 8 (computed)

How this code was found

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

[[660,18,30]]: distance revision of the board's [[660,18,30]] entry

Revision history

The entry keeps its parameters [[660,18,30]]. The code, its checks, its layout, and its original provenance are unchanged; only the distance block is corrected. A GPU random-information-set search (verify/ris_gpu.py, recover mode, 300,000,000 trials per side, pair depth 0, seed 4101) exhibits a weight-45 X logical, so the previous witness-backed bound was overstated on that side; the overall distance d = 30 is unchanged. Each lighter witness is carried in the entry with the budget it was found at; the other side keeps its original witness where it was not refuted. Distance remains an upper bound, not an exact claim.

Evidence

Every GPU proposal was re-validated on the CPU against the committed check matrices (in the kernel of the opposite side's checks, outside the row space of its own side) before it was recorded. The pass is the weekly fresh-seed re-measurement of the board's cell leaders (issue 2025, run of 2026-09-24); every recorded reading is the lightest CPU-verified logical at that budget.

| side | seed | claimed | GPU best weight | CPU-verified witness | trials | |---|---|---|---|---|---| | X | 4101 | 80 | 45 | 45 | 300,000,000 | | Z | 4101 | 30 | 30 | 30 | 300,000,000 | | X | 4102 | 80 | 45 | 45 | 300,000,000 | | Z | 4102 | 30 | 30 | 30 | 300,000,000 |

Original note, with the file paths updated

[[660,18,30]] - metacyclic generalized-bicycle code

Direction & hypothesis

The target was the unrestricted / weight-8 frontier. The board contains [[672,18,30]] with the same k, witnessed d, and maximum check weight, so a code with the same three quantities at smaller n would advance that frontier. The search used the non-abelian metacyclic 2BGA/lifted-product family because its group action provides more generator choices than an abelian bicycle while keeping CSS commutation automatic.

What was searched

The generator was the regular two-block construction H_X = [L(a) | R(b)] and H_Z = [R(b)^T | L(a)^T] over C_22 semidirect C_15 with action r = 5. I drew 1,200 distinct weight-4 support pairs from 2,024 metacyclic parameter triples with group order 60 through 350. Every candidate was checked for CSS commutation, recomputed k, maximum check weight, and screened with the accelerated RIS surrogate at 120 trials. A persistent archive was deduplicated by the verifier-compatible stabilizer fingerprint; 660 candidates survived the screen with k >= 4 and d >= 8. The submitted support pair was the best screen record after the non-dominated archive was formed.

Evidence trail

All distance values below are upper bounds from explicit logical witnesses.

| RIS trials | lightest d found | | ---: | ---: | | 120 screen | 103 | | 10,000 | 90 | | 100,000 | 42 | | 1,000,000 | 36 | | 2,000,000 | 30 | | 5,000,000 | 30 |

The 1M run still returned 36. The independent 2M and 5M runs used separate seeds and both returned a weight-30 Z-type logical, so the bound settled at d <= 30 by 2M and held at 5M. The final CLI packaging search independently extracted witnesses for both CSS sides, then the repository verifier checked n = 660, k = 18, CSS commutation, maximum check weight 8, and witness validity. The submitted confidence is upper_bound: the evidence is d <= 30, not an exact distance proof.

Dead ends

The shallow leaders were not promoted. At 100k trials, the best screen records collapsed to distances 14, 18, 22, 24, 30, and 36. This is consistent with the repository's warning that large-block RIS readings inflate at low trial depth. The metacyclic route was therefore narrowed to the one candidate that remained frontier-relevant after the 1M, 2M, and 5M ladder.

Tools

Model: GPT-5. Repo tooling: the metacyclic and 2BGA constructors in research/kit/group_algebra.py, the accelerated RIS surrogate, the qldpc submission CLI, and the trusted verifier. No files under verify/ were changed.

Reproduction

Build the group and supports with:

from research.kit.group_algebra import build_2bga, metacyclic

mul, _ = metacyclic(22, 15, 5)
HX, HZ = build_2bga(
    mul,
    [18, 142, 163, 293],
    [73, 147, 201, 215],
)

This gives 330 checks per side, 660 qubits, k = 18, and row weight 8.

Parity checks

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