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[[700,44,16]] d ≤
n
700
k
44
d
16
kd²/n
16.091
w
7
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 16, d_Z ≤ 16 · w_X = 7, w_Z = 7 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 16 · witness weight 16 (claimed upper_bound)
witness operator (support, 16 qubits)
[28, 45, 64, 81, 261, 262, 297, 298, 544, 557, 590, 607, 622, 635, 685, 696]
d_Z 16 · witness weight 16 (claimed upper_bound)
witness operator (support, 16 qubits)
[67, 68, 81, 82, 174, 178, 181, 188, 192, 195, 284, 287, 298, 301, 397, 411]
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 7 · H_Z 7
qubit degrees H_X 3–4 (mean 3.36) · H_Z 3–4 (mean 3.36)
trapping sets H_X (1,3)×448 (2,2)×112 (3,3)×784 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,3): 448 (1,4): 252 (2,2): 112 (2,4): 1792 (2,5): 4032 (2,6): 1008 (3,3): 784 (3,4): 672 (3,5): 9744 (3,6): 46368 (3,7): 37184 (3,8): 11424 (3,9): 4032 (3,10): 336
trapping sets H_Z (1,3)×448 (2,4)×2100 (3,5)×13440 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,3): 448 (1,4): 252 (2,4): 2100 (2,5): 4032 (2,6): 840 (3,5): 13440 (3,6): 49140 (3,7): 34272 (3,8): 10164 (3,9): 3360 (3,10): 168

Construction & provenance

authors @mathysrennela
provenance submitted through the challenge
novelty novelty not audited
construction Lifted product over Z_t x Z_2 (|G| = 2t). Protograph A (3x4), B (3x4) from arXiv:2606.24808 Table 1 (R3EliteP02, an SCE-search elite), x-exponents reduced modulo the family parameter t=14 to fit the n<=700 cap: n = (nA*nB + mA*mB)*|G| = 25*28 = 700. A entries act by the left regular representation, B entries by the right regular representation (via inverse); HX = [A~ (x) I_4 | I_3 (x) B~^T], HZ = [I_4 (x) B~ | A~^T (x) I_3] (protograph-level Kronecker, expanded block transposes in HZ). The paper reports [[1500,76,<=20]] at t=30; this is the same protograph at a smaller lift. Distance is a witness-backed upper bound (randomized information-set search).
model GLM 5.3 Flash (claimed, not verified)
builds on arXiv:2606.24808
date 2026-09-14
notes Construction family and protograph published in arXiv:2606.24808 (R3EliteP02 at t=30, reported [[1500,76,<=20]]); this entry is the same protograph at a new, smaller lift (t=14), a parameter point the paper does not tabulate; literature novelty of the parameter set unverified. Board dedup gate-checked: not an exact or WL-equivalent duplicate of any existing entry.
family lifted product (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

[[700,44,16]] lifted product over Z_14 x Z_2, SCE-paper protograph R3EliteP02 at t=14

Direction & hypothesis

Cell: unrestricted / weight-8 (max check weight 7: the protograph row weight is nA + mB = 4 + 3 = 7). Family: lifted-product over the abelian group Z_t x Z_2, protograph transcribed from arXiv:2606.24808 (Table 1 and Supplemental S7, code R3EliteP02). The paper's families are scalable, n = (nA*nB + mA*mB)*|G|, so the same protograph instantiated below the board's n <= 700 cap may land non-dominated instances in the high-rate band of the weight-8 cell.

What was searched

All 8 Table-1 protograph families of the paper were swept over every group parameter with n <= 700: 40 instantiations (abelian Z_3 x Z_t, Z_2 x Z_2 x Z_t, Z_t x Z_2; non-abelian dicyclic Dic_m and dihedral D_m lifts), each built, CSS-checked, k computed exactly over GF(2), and screened at 3000 RIS trials per candidate. Only the two Z_t x Z_2 families (R3EliteP01, R3EliteP02) survive below the cap: the six weight-8 families collapse to d <= 4-8 at every sub-cap size and are Pareto-dominated. At odd t the group Z_t x Z_2 is cyclic and the lift degenerates (the paper observes this too), so only even t were eligible.

Evidence trail

  • Screening: d <= 16 at 3000 RIS trials.
  • Submission witnesses (20000 RIS trials per side): lightest X-logical

    • weight 16, lightest Z-logical weight 16; claim d <= 16, confidence upper_bound.

  • Staging gate (the repo's validate_candidate): passed; refutation, 8000 RIS

    • trials, found no lighter logical; not an exact or WL-equivalent duplicate of any board entry; labeled board-advancing in the cell unrestricted x weight-8; kd^2/n = 16.09.

  • Claim: upper bound d <= 16, witness-backed, not exact (k = 44 is far above

    • the certification envelope of d <= 13, k <= 12).

Dead ends

The six weight-8 protograph families (R1Elite01, R1Elite02, R2Elite01, R2Elite02, R3Elite01, R3Elite02) collapse at sub-cap lifts: every instantiation screened d <= 4-8 and was dominated. The paper's designs only pay off near n ~ 1500; its QDistRnd upper bounds do not survive the 2-5x block-length reduction. Sibling shadowing: at t = 8 the P01 protograph (k = 35) strictly dominates the P02 one (k = 32) at equal n, d, w; only the P01 instance was carried forward.

Tools

Model: GLM 5.3 Flash (agent harness: Zed). Tooling: a general matrix-protograph lifted-product constructor written for this campaign and self-tested to reproduce the paper's stated (n, k) for all 8 Table-1 codes at the paper's own group parameters; the repo's GF(2) rank/RIS stack; the repo's validation gate. Screening budget ~3000 trials per candidate.

Reproduction

G = Z_t x Z_2 with t = 14 (x mod 14, y mod 2), q = |G| = 28, n = (nA*nB + mA*mB)*q = 25*28 = 700. Protograph (arXiv:2606.24808 S7, R3EliteP02; entry notation x^a y^b, e = x^0 y^0):

A (3x4) = [[x^6 y, x^6, x^6 y, x^6 ], [e, x, x^2, x^26 ], [x^24 y, x^26, x^21 y, x^23 ]] B (3x4) = [[x^29 y, x^13, x^8 y, x^3 ], [x^10, x^6, x^2, x^28 ], [x^2 y, x^29, x^26 y, x^12 ]]

with every x-exponent reduced mod 14 (y mod 2). Build the lifted product of arXiv:2606.24808 Eq. (S4): expand each A entry by the left regular representation and each B entry by the right regular representation (via the inverse) into q x q permutation blocks; then

HX = [A~ (x) I_4 | I_3 (x) B~^T], HZ = [I_4 (x) B~ | A~^T (x) I_3]

taken at the protograph level, where the block transposes in HZ are expanded transposes of the q x q blocks. CSS commutation is automatic (left and right regular representations commute); k = n - rank(HX) - rank(HZ) = 44 over GF(2), max check weight 7.

Parity checks

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