← back to the board
[[698,2,79]] d ≤
n
698
k
2
d
79
kd²/n
17.883
w
8
X/Z
1.03

Share this result

Distance

X/Z asymmetry 1.03 · d_X ≤ 81, d_Z ≤ 79 · 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 81 · witness weight 81 (claimed upper_bound)
witness operator (support, 81 qubits)
[1, 2, 19, 21, 31, 35, 36, 39, 41, 57, 59, 61, 70, 91, 96, 109, 110, 116, 128, 131, 137, 162, 168, 172, 175, 177, 182, 199, 200, 205, 217, 218, 219, 227, 247, 254, 281, 289, 291, 294, 296, 314, 316, 329, 334, 360, 379, 384, 394, 402, 412, 422, 437, 448, 455, 478, 481, 483, 486, 495, 498, 505, 517, 528, 537, 557, 567, 569, 583, 599, 615, 619, 624, 626, 634, 648, 649, 650, 663, 665, 685]
d_Z 79 · witness weight 79 (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, 79 qubits)
[0, 2, 4, 7, 24, 33, 35, 38, 42, 45, 54, 57, 59, 64, 68, 76, 87, 92, 97, 100, 104, 123, 125, 128, 130, 133, 137, 142, 152, 156, 159, 163, 166, 168, 189, 190, 192, 194, 201, 202, 204, 206, 209, 216, 220, 228, 232, 235, 239, 242, 244, 246, 249, 268, 273, 282, 285, 287, 292, 294, 296, 299, 304, 322, 323, 325, 330, 332, 344, 350, 379, 385, 455, 562, 590, 595, 605, 671, 697]
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 6 · H_Z 6 (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)×698 (2,6)×9772 (3,6)×2792 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,4): 698 (2,6): 9772 (3,6): 2792 (3,8): 196836 (3,10): 19544
trapping sets H_Z (1,4)×698 (2,6)×9772 (3,6)×2792 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,4): 698 (2,6): 9772 (3,6): 2792 (3,8): 196836 (3,10): 19544

Construction & provenance

authors @vprusso
provenance submitted through the challenge
novelty known parameter set; see provenance notes
construction Cyclic generalized-bicycle code on the ring x349 - 1 with a(x) = x58 + x134 + x184 + x305, b(x) = x29 + x103 + x323 + x343; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T].
model Claude Claude Opus 5 (claimed, not verified)
date 2026-09-22
notes Found by a randomized sweep over sparse polynomial pairs, screened against the live board before any expensive work. Checked for single-block logicals via the ideal generated by (x^m - 1)/gcd(a, x^m - 1) before the distance was believed.
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

[[698,2,79]]: distance revision of the board's [[698,2,81]] entry

Revision history

[[698,2,79]] supersedes the board's [[698,2,81]] entry. 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 4102) exhibits a weight-79 Z logical, so the previous witness-backed bound was overstated and the honest parameter set is [[698,2,79]]. The headline falls from kd^2/n = 18.8 to 17.88. 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 | 81 | 85 | 85 | 300,000,000 | | Z | 4101 | 81 | 81 | 81 | 300,000,000 | | X | 4102 | 81 | 91 | 91 | 300,000,000 | | Z | 4102 | 81 | 79 | 79 | 300,000,000 |

Original note, with the file paths updated

[[698,2,81]] weight-8 cyclic generalized-bicycle

Hypothesis

Cyclic generalized-bicycle codes at check weight 8 cover a wide blocklength range, and the board's coverage of that range is uneven: there are stretches of n where no entry sits near the (k, d) the family can reach. A broad randomized sweep over sparse polynomial pairs, screened against the live board before any expensive work, finds the gaps.

Construction

ring x^349 - 1 a(x) = x^58 + x^134 + x^184 + x^305 b(x) = x^29 + x^103 + x^323 + x^343 H_X = [circ(a) | circ(b)] H_Z = [circ(b)^T | circ(a)^T]

n = 2m, and k = 2 deg gcd(a, b, x^m - 1), computed by Euclid before any matrix work so that most draws are discarded for free.

What was swept

One loop draws a ring size and a weight split, samples the two sparse polynomials, computes k by Euclid, and runs a cheap 60k-trial distance screen. A draw survives only if the resulting (n, k, d, w) is undominated on the live board snapshot. Surviving draws go through an escalating ladder of 400k, 2M and 8M random information-set trials, with the board comparison repeated at each rung so a candidate that collapses is dropped as soon as it stops being interesting.

The single-block check

General RIS over all 2m columns is close to blind to a logical supported entirely on one block. Such a vector u satisfies a(x) u(x) = 0 mod x^m - 1, which puts u in the ideal generated by h = (x^m - 1) / gcd(a, x^m - 1), so it can be searched directly in a space of dimension deg h rather than 2m. This matters: a previous submission of mine survived 150M general RIS trials at weight 74 and was then refuted by a weight-64 logical sitting entirely in one block, which the ideal search finds in seconds. Every candidate here is checked that way before the distance is believed, and any candidate whose single-block bound comes in below the ladder is dropped rather than submitted.

Distance ladder

Witness search runs on each side separately, so a run that happens to find one side cannot leave the other without a witness. Both witnesses are re-checked directly against H: in the kernel of the opposite matrix, and outside the row space of its own.

What it advances

Score kd^2/n = 18.799 at check weight 8. Undominated in its cell against the board at submission time.

Boundary

The distance is an upper bound from witness search, not a proof. Literature novelty is unverified: cyclic GB codes are a classical family and these parameters may appear in the 2BGA literature.

Parity checks

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