← back to the board
[[330,50,30]] d ≤
n
330
k
50
d
30
kd²/n
136.364
w
16
X/Z
1

Share this result

Distance

X/Z asymmetry 1 · d_X ≤ 30, d_Z ≤ 30 · w_X = 16, w_Z = 16 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 30 · witness weight 30 (claimed upper_bound)
witness found by @vprusso · research/kit/surrogate.lightest_logical · found at 400 trials · survived 400 trials · 2026-10-15
witness operator (support, 30 qubits)
[1, 8, 16, 44, 53, 54, 61, 70, 71, 83, 91, 94, 99, 103, 116, 120, 128, 135, 159, 165, 185, 237, 246, 270, 284, 288, 300, 304, 308, 312]
d_Z 30 · witness weight 30 (claimed upper_bound)
witness found by @vprusso · research/kit/surrogate.lightest_logical · found at 400 trials · survived 400 trials · 2026-10-15
witness operator (support, 30 qubits)
[23, 34, 40, 44, 51, 60, 69, 82, 101, 106, 120, 123, 129, 135, 154, 156, 173, 180, 208, 210, 231, 240, 243, 251, 257, 260, 269, 271, 290, 305]
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 16 · H_Z 16
qubit degrees H_X 6–10 (mean 8.0) · H_Z 6–10 (mean 8.0)
trapping sets H_X (1,6)×165 (2,8)×165 (smallest syndrome weight at each size, connected sets of up to 3 qubits; sizes above 2 skipped under the cost cap)
full (size, syndrome weight): count census for H_X
(1,6): 165 (1,10): 165 (2,8): 165 (2,10): 2145 (2,12): 990 (2,14): 8085 (2,16): 660 (2,18): 5610
trapping sets H_Z (1,6)×165 (2,8)×165 (smallest syndrome weight at each size, connected sets of up to 3 qubits; sizes above 2 skipped under the cost cap)
full (size, syndrome weight): count census for H_Z
(1,6): 165 (1,10): 165 (2,8): 165 (2,10): 2145 (2,12): 990 (2,14): 8085 (2,16): 660 (2,18): 5610

Construction & provenance

authors @vprusso
provenance submitted through the challenge
novelty novelty not audited
construction Cyclic generalized bicycle at m=165 = 3 x 5 x 11, with ord_2(m)=20, so x165 - 1 factors over GF(2) into 14 cyclotomic cosets, 1 of size 1, 1 of size 2, 3 of size 4, 3 of size 10, 6 of size 20. The divisor g is assembled from coset minimal polynomials to degree 25, which fixes k = 2 deg g = 50 by construction, and (a,b) was drawn from the ideal (g) by information-set decoding over sparse supports, keeping weight 10 and weight 6 in the two blocks. Both weights are even, so x+1 divides the gcd; x+1 is x1 - 1, so the only block logical this forces has weight m and is far above the claim. m is composite, so the quotient fold acts at t=3, t=5, t=11, t=15, t=33 and t=55; a fold over every equal-orbit partition of the qubits returns nothing lighter than 42, clear of the claim. H_X = [circ(a) | circ(b)] and H_Z = [circ(b)^T | circ(a)^T] on n = 2m = 330 qubits at uniform row weight 16, with a = [4, 37, 50, 65, 82, 103, 107, 116, 130, 134] and b = [11, 76, 102, 106, 126, 135].
model Claude Claude Opus 5 (claimed, not verified)
date 2026-10-15
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

--- author: "@vprusso" ---

[[330,50,30]]: cyclic generalized-bicycle code at m = 165, row weight 16

At row weight 16 or lighter, the best distance on the board with n <= 330 and k >= 50 is 21, at [[254,58,21]]. This entry reaches 30, and since that same entry is also the best at any row weight in the range, the entry clears the unrestricted comparison too.

Direction & hypothesis

m = 165 had never been swept for this construction. n = 330 holds 19 board entries, but none at this dimension and row weight.

For a cyclic generalized bicycle on x^m - 1 the dimension is k = 2 deg gcd(a, b, x^m - 1), so it can be set in advance: build a divisor g of chosen degree from cyclotomic coset minimal polynomials and draw a and b as low-weight codewords of its ideal. The degree matters more narrowly than it looks. Every candidate this construction produced in the same session sits at deg g / m between 0.117 and 0.152, and degrees above about 0.17 land in a high-rate region where the family returns distance 4 or 5 whatever the modulus. Degree 25 at m = 165 is 0.152, at the top of the usable band.

What was searched

m = 165 = 3 x 5 x 11 with ord_2(165) = 20, so x^165 - 1 factors over GF(2) into 14 cyclotomic cosets: one of size 1, one of size 2, three of size 4, three of size 10 and six of size 20. Reachable divisor degrees are the subset sums of those sizes. The divisor used here has degree 25, which fixes k = 50.

Degrees were filtered on three conditions before any cores were spent. The degree must be a sum of coset sizes, or the divisor does not exist and the sweep skips it silently. The chosen cosets must include the size-1 coset at the origin, or almost every draw is lost to a parity rejection, since the information-set draw returns two even weights most of the time. And the chosen exponents must not share a common factor with m, or the divisor sits inside x^q - 1 for a proper divisor q of m, the ideal fills with weight-2 elements and the resulting codes fall below distance 4.

The sweep ran at 20,000 information-set trials per draw. At this (n, k) the sweep produced draws at row weights 16 and 18; a probe at 600,000 trials over 4 seeds read 33 at weight 16 and 35 at weight 18. Both then fell to 32 under their deep runs, at which point the weight-16 draw dominates the weight-18 one outright, on equal n, equal distance, higher k and lighter weight. Only the weight-16 draw is submitted.

The polynomial weights are 10 and 6, so (x + 1) divides the common gcd. Since x + 1 is x^1 - 1, the only block logical that forces has weight 165, far above the claim.

Evidence trail

deg gcd(a, x^165 - 1) = deg gcd(b, x^165 - 1) = deg gcd(a, b, x^165 - 1) = 25, so the leak between the two single-block kernels and k is 0 on both sides.

A 24-seed gate at 2,000,000 information-set trials per seed settled at 30, with per-seed readings from 30 to 35 and three of the 24 seeds reaching the minimum. A single uninterrupted run of 8,000,000 trials, matching the depth the verifier's own refutation pass reaches, read 32, above the gate, so the gate is the binding instrument and the claim is 30.

The single-block logicals form the cyclic code of dimension 25 whose zeros are the 140 residues the divisor omits. The longest run of consecutive residues among them is 28, so the Bose-Chaudhuri-Hocquenghem bound puts the lightest single-block logical at 29 or above, and a direct search confined to one circulant block at 12 seeds of 600,000 trials independently finds nothing below 33. The quotient fold acts at t = 3, 5, 11, 15, 33 and 55; a fold over every equal-orbit partition of the qubits returns nothing lighter than 42, so none of the six folds binds.

The claim is a witness-backed upper bound, not certified. Both witnesses weigh 30, both were found by the gate rather than carried across by the construction's symmetry, and both commute with the opposite check matrix and lie outside its row space.

Dead ends

The 20,000-trial screen overstates this family. This draw screened at 40, probed to 33 and gated to 30, so the screen was 10 above the claim.

Three other dimensions at this modulus were measured and none survived. [[330,46]] at row weight 18 reached 32 and is dominated by this entry. [[330,42]] at row weight 16 probed to 24 against a threshold of 24, so it advances by nothing. [[330,38]] at row weight 18 carried a recorded distance of 33 that came from a structural bound rather than a search, and a 2,400,000-trial probe read 34, so the bound caps the code below anything a witness can certify and that cell is finished.

The same session priced two cells at m = 267 the same way, [[534,68]] at row weight 20 and [[534,70]] at row weight 14, and both died: the first to an orbit fold that capped it at 57 through an x^89-invariant partition after it had already probed to 69 with a witness, the second to a bound of 54 that a 2,400,000-trial probe could not reach, reading 68.

Tools

Claude Opus 5 driving a Claude Code session. Distance readings, witness validation and the single-block searches come from this repository's verify/gf2_fast extension. Divisor assembly, coset selection, the information-set draws and the orbit fold are session tooling outside this repository, described above in enough detail to rewrite. Roughly two core-hours for the gate, one for the 8,000,000-trial run, and a few minutes each for the screen and the fold.

Reproduction

m = 165, n = 2m = 330. With a = {4, 37, 50, 65, 82, 103, 107, 116, 130, 134} and b = {11, 76, 102, 106, 126, 135} as exponent sets,

H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T]

where circ(s)[i, (i + e) mod m] = 1 for each e in s. The divisor is recovered as gcd(a, b, x^165 - 1), of degree 25. The submitted codes/330-50-30.json carries both matrices row by row and both distance witnesses.

Parity checks

X-checks 165 (max weight 16) · Z-checks 165 (max weight 16)
H_X (165 checks, sparse supports)
[4, 37, 50, 65, 82, 103, 107, 116, 130, 134, 176, 241, 267, 271, 291, 300] [5, 38, 51, 66, 83, 104, 108, 117, 131, 135, 177, 242, 268, 272, 292, 301] [6, 39, 52, 67, 84, 105, 109, 118, 132, 136, 178, 243, 269, 273, 293, 302] [7, 40, 53, 68, 85, 106, 110, 119, 133, 137, 179, 244, 270, 274, 294, 303] [8, 41, 54, 69, 86, 107, 111, 120, 134, 138, 180, 245, 271, 275, 295, 304] [9, 42, 55, 70, 87, 108, 112, 121, 135, 139, 181, 246, 272, 276, 296, 305] [10, 43, 56, 71, 88, 109, 113, 122, 136, 140, 182, 247, 273, 277, 297, 306] [11, 44, 57, 72, 89, 110, 114, 123, 137, 141, 183, 248, 274, 278, 298, 307] [12, 45, 58, 73, 90, 111, 115, 124, 138, 142, 184, 249, 275, 279, 299, 308] [13, 46, 59, 74, 91, 112, 116, 125, 139, 143, 185, 250, 276, 280, 300, 309] [14, 47, 60, 75, 92, 113, 117, 126, 140, 144, 186, 251, 277, 281, 301, 310] [15, 48, 61, 76, 93, 114, 118, 127, 141, 145, 187, 252, 278, 282, 302, 311] [16, 49, 62, 77, 94, 115, 119, 128, 142, 146, 188, 253, 279, 283, 303, 312] [17, 50, 63, 78, 95, 116, 120, 129, 143, 147, 189, 254, 280, 284, 304, 313] [18, 51, 64, 79, 96, 117, 121, 130, 144, 148, 190, 255, 281, 285, 305, 314] [19, 52, 65, 80, 97, 118, 122, 131, 145, 149, 191, 256, 282, 286, 306, 315] [20, 53, 66, 81, 98, 119, 123, 132, 146, 150, 192, 257, 283, 287, 307, 316] [21, 54, 67, 82, 99, 120, 124, 133, 147, 151, 193, 258, 284, 288, 308, 317] [22, 55, 68, 83, 100, 121, 125, 134, 148, 152, 194, 259, 285, 289, 309, 318] [23, 56, 69, 84, 101, 122, 126, 135, 149, 153, 195, 260, 286, 290, 310, 319] [24, 57, 70, 85, 102, 123, 127, 136, 150, 154, 196, 261, 287, 291, 311, 320] [25, 58, 71, 86, 103, 124, 128, 137, 151, 155, 197, 262, 288, 292, 312, 321] [26, 59, 72, 87, 104, 125, 129, 138, 152, 156, 198, 263, 289, 293, 313, 322] [27, 60, 73, 88, 105, 126, 130, 139, 153, 157, 199, 264, 290, 294, 314, 323] [28, 61, 74, 89, 106, 127, 131, 140, 154, 158, 200, 265, 291, 295, 315, 324] [29, 62, 75, 90, 107, 128, 132, 141, 155, 159, 201, 266, 292, 296, 316, 325] [30, 63, 76, 91, 108, 129, 133, 142, 156, 160, 202, 267, 293, 297, 317, 326] [31, 64, 77, 92, 109, 130, 134, 143, 157, 161, 203, 268, 294, 298, 318, 327] [32, 65, 78, 93, 110, 131, 135, 144, 158, 162, 204, 269, 295, 299, 319, 328] [33, 66, 79, 94, 111, 132, 136, 145, 159, 163, 205, 270, 296, 300, 320, 329] [34, 67, 80, 95, 112, 133, 137, 146, 160, 164, 165, 206, 271, 297, 301, 321] [0, 35, 68, 81, 96, 113, 134, 138, 147, 161, 166, 207, 272, 298, 302, 322] [1, 36, 69, 82, 97, 114, 135, 139, 148, 162, 167, 208, 273, 299, 303, 323] [2, 37, 70, 83, 98, 115, 136, 140, 149, 163, 168, 209, 274, 300, 304, 324] [3, 38, 71, 84, 99, 116, 137, 141, 150, 164, 169, 210, 275, 301, 305, 325] [0, 4, 39, 72, 85, 100, 117, 138, 142, 151, 170, 211, 276, 302, 306, 326] [1, 5, 40, 73, 86, 101, 118, 139, 143, 152, 171, 212, 277, 303, 307, 327] [2, 6, 41, 74, 87, 102, 119, 140, 144, 153, 172, 213, 278, 304, 308, 328] [3, 7, 42, 75, 88, 103, 120, 141, 145, 154, 173, 214, 279, 305, 309, 329] [4, 8, 43, 76, 89, 104, 121, 142, 146, 155, 165, 174, 215, 280, 306, 310] [5, 9, 44, 77, 90, 105, 122, 143, 147, 156, 166, 175, 216, 281, 307, 311] [6, 10, 45, 78, 91, 106, 123, 144, 148, 157, 167, 176, 217, 282, 308, 312] [7, 11, 46, 79, 92, 107, 124, 145, 149, 158, 168, 177, 218, 283, 309, 313] [8, 12, 47, 80, 93, 108, 125, 146, 150, 159, 169, 178, 219, 284, 310, 314] [9, 13, 48, 81, 94, 109, 126, 147, 151, 160, 170, 179, 220, 285, 311, 315] [10, 14, 49, 82, 95, 110, 127, 148, 152, 161, 171, 180, 221, 286, 312, 316] [11, 15, 50, 83, 96, 111, 128, 149, 153, 162, 172, 181, 222, 287, 313, 317] [12, 16, 51, 84, 97, 112, 129, 150, 154, 163, 173, 182, 223, 288, 314, 318] [13, 17, 52, 85, 98, 113, 130, 151, 155, 164, 174, 183, 224, 289, 315, 319] [0, 14, 18, 53, 86, 99, 114, 131, 152, 156, 175, 184, 225, 290, 316, 320] [1, 15, 19, 54, 87, 100, 115, 132, 153, 157, 176, 185, 226, 291, 317, 321] [2, 16, 20, 55, 88, 101, 116, 133, 154, 158, 177, 186, 227, 292, 318, 322] [3, 17, 21, 56, 89, 102, 117, 134, 155, 159, 178, 187, 228, 293, 319, 323] [4, 18, 22, 57, 90, 103, 118, 135, 156, 160, 179, 188, 229, 294, 320, 324] [5, 19, 23, 58, 91, 104, 119, 136, 157, 161, 180, 189, 230, 295, 321, 325] [6, 20, 24, 59, 92, 105, 120, 137, 158, 162, 181, 190, 231, 296, 322, 326] [7, 21, 25, 60, 93, 106, 121, 138, 159, 163, 182, 191, 232, 297, 323, 327] [8, 22, 26, 61, 94, 107, 122, 139, 160, 164, 183, 192, 233, 298, 324, 328] [0, 9, 23, 27, 62, 95, 108, 123, 140, 161, 184, 193, 234, 299, 325, 329] [1, 10, 24, 28, 63, 96, 109, 124, 141, 162, 165, 185, 194, 235, 300, 326] [2, 11, 25, 29, 64, 97, 110, 125, 142, 163, 166, 186, 195, 236, 301, 327] [3, 12, 26, 30, 65, 98, 111, 126, 143, 164, 167, 187, 196, 237, 302, 328] [0, 4, 13, 27, 31, 66, 99, 112, 127, 144, 168, 188, 197, 238, 303, 329] [1, 5, 14, 28, 32, 67, 100, 113, 128, 145, 165, 169, 189, 198, 239, 304] [2, 6, 15, 29, 33, 68, 101, 114, 129, 146, 166, 170, 190, 199, 240, 305] [3, 7, 16, 30, 34, 69, 102, 115, 130, 147, 167, 171, 191, 200, 241, 306] [4, 8, 17, 31, 35, 70, 103, 116, 131, 148, 168, 172, 192, 201, 242, 307] [5, 9, 18, 32, 36, 71, 104, 117, 132, 149, 169, 173, 193, 202, 243, 308] [6, 10, 19, 33, 37, 72, 105, 118, 133, 150, 170, 174, 194, 203, 244, 309] [7, 11, 20, 34, 38, 73, 106, 119, 134, 151, 171, 175, 195, 204, 245, 310] [8, 12, 21, 35, 39, 74, 107, 120, 135, 152, 172, 176, 196, 205, 246, 311] [9, 13, 22, 36, 40, 75, 108, 121, 136, 153, 173, 177, 197, 206, 247, 312] [10, 14, 23, 37, 41, 76, 109, 122, 137, 154, 174, 178, 198, 207, 248, 313] [11, 15, 24, 38, 42, 77, 110, 123, 138, 155, 175, 179, 199, 208, 249, 314] [12, 16, 25, 39, 43, 78, 111, 124, 139, 156, 176, 180, 200, 209, 250, 315] [13, 17, 26, 40, 44, 79, 112, 125, 140, 157, 177, 181, 201, 210, 251, 316] [14, 18, 27, 41, 45, 80, 113, 126, 141, 158, 178, 182, 202, 211, 252, 317] [15, 19, 28, 42, 46, 81, 114, 127, 142, 159, 179, 183, 203, 212, 253, 318] [16, 20, 29, 43, 47, 82, 115, 128, 143, 160, 180, 184, 204, 213, 254, 319] [17, 21, 30, 44, 48, 83, 116, 129, 144, 161, 181, 185, 205, 214, 255, 320] [18, 22, 31, 45, 49, 84, 117, 130, 145, 162, 182, 186, 206, 215, 256, 321] [19, 23, 32, 46, 50, 85, 118, 131, 146, 163, 183, 187, 207, 216, 257, 322] [20, 24, 33, 47, 51, 86, 119, 132, 147, 164, 184, 188, 208, 217, 258, 323] [0, 21, 25, 34, 48, 52, 87, 120, 133, 148, 185, 189, 209, 218, 259, 324] [1, 22, 26, 35, 49, 53, 88, 121, 134, 149, 186, 190, 210, 219, 260, 325] [2, 23, 27, 36, 50, 54, 89, 122, 135, 150, 187, 191, 211, 220, 261, 326] [3, 24, 28, 37, 51, 55, 90, 123, 136, 151, 188, 192, 212, 221, 262, 327] [4, 25, 29, 38, 52, 56, 91, 124, 137, 152, 189, 193, 213, 222, 263, 328] [5, 26, 30, 39, 53, 57, 92, 125, 138, 153, 190, 194, 214, 223, 264, 329] [6, 27, 31, 40, 54, 58, 93, 126, 139, 154, 165, 191, 195, 215, 224, 265] [7, 28, 32, 41, 55, 59, 94, 127, 140, 155, 166, 192, 196, 216, 225, 266] [8, 29, 33, 42, 56, 60, 95, 128, 141, 156, 167, 193, 197, 217, 226, 267] [9, 30, 34, 43, 57, 61, 96, 129, 142, 157, 168, 194, 198, 218, 227, 268] [10, 31, 35, 44, 58, 62, 97, 130, 143, 158, 169, 195, 199, 219, 228, 269] [11, 32, 36, 45, 59, 63, 98, 131, 144, 159, 170, 196, 200, 220, 229, 270] [12, 33, 37, 46, 60, 64, 99, 132, 145, 160, 171, 197, 201, 221, 230, 271] [13, 34, 38, 47, 61, 65, 100, 133, 146, 161, 172, 198, 202, 222, 231, 272] [14, 35, 39, 48, 62, 66, 101, 134, 147, 162, 173, 199, 203, 223, 232, 273] [15, 36, 40, 49, 63, 67, 102, 135, 148, 163, 174, 200, 204, 224, 233, 274] [16, 37, 41, 50, 64, 68, 103, 136, 149, 164, 175, 201, 205, 225, 234, 275] [0, 17, 38, 42, 51, 65, 69, 104, 137, 150, 176, 202, 206, 226, 235, 276] [1, 18, 39, 43, 52, 66, 70, 105, 138, 151, 177, 203, 207, 227, 236, 277] [2, 19, 40, 44, 53, 67, 71, 106, 139, 152, 178, 204, 208, 228, 237, 278] [3, 20, 41, 45, 54, 68, 72, 107, 140, 153, 179, 205, 209, 229, 238, 279] [4, 21, 42, 46, 55, 69, 73, 108, 141, 154, 180, 206, 210, 230, 239, 280] [5, 22, 43, 47, 56, 70, 74, 109, 142, 155, 181, 207, 211, 231, 240, 281] [6, 23, 44, 48, 57, 71, 75, 110, 143, 156, 182, 208, 212, 232, 241, 282] [7, 24, 45, 49, 58, 72, 76, 111, 144, 157, 183, 209, 213, 233, 242, 283] [8, 25, 46, 50, 59, 73, 77, 112, 145, 158, 184, 210, 214, 234, 243, 284] [9, 26, 47, 51, 60, 74, 78, 113, 146, 159, 185, 211, 215, 235, 244, 285] [10, 27, 48, 52, 61, 75, 79, 114, 147, 160, 186, 212, 216, 236, 245, 286] [11, 28, 49, 53, 62, 76, 80, 115, 148, 161, 187, 213, 217, 237, 246, 287] [12, 29, 50, 54, 63, 77, 81, 116, 149, 162, 188, 214, 218, 238, 247, 288] [13, 30, 51, 55, 64, 78, 82, 117, 150, 163, 189, 215, 219, 239, 248, 289] [14, 31, 52, 56, 65, 79, 83, 118, 151, 164, 190, 216, 220, 240, 249, 290] [0, 15, 32, 53, 57, 66, 80, 84, 119, 152, 191, 217, 221, 241, 250, 291] [1, 16, 33, 54, 58, 67, 81, 85, 120, 153, 192, 218, 222, 242, 251, 292] [2, 17, 34, 55, 59, 68, 82, 86, 121, 154, 193, 219, 223, 243, 252, 293] [3, 18, 35, 56, 60, 69, 83, 87, 122, 155, 194, 220, 224, 244, 253, 294] [4, 19, 36, 57, 61, 70, 84, 88, 123, 156, 195, 221, 225, 245, 254, 295] [5, 20, 37, 58, 62, 71, 85, 89, 124, 157, 196, 222, 226, 246, 255, 296] [6, 21, 38, 59, 63, 72, 86, 90, 125, 158, 197, 223, 227, 247, 256, 297] [7, 22, 39, 60, 64, 73, 87, 91, 126, 159, 198, 224, 228, 248, 257, 298] [8, 23, 40, 61, 65, 74, 88, 92, 127, 160, 199, 225, 229, 249, 258, 299] [9, 24, 41, 62, 66, 75, 89, 93, 128, 161, 200, 226, 230, 250, 259, 300] [10, 25, 42, 63, 67, 76, 90, 94, 129, 162, 201, 227, 231, 251, 260, 301] [11, 26, 43, 64, 68, 77, 91, 95, 130, 163, 202, 228, 232, 252, 261, 302] [12, 27, 44, 65, 69, 78, 92, 96, 131, 164, 203, 229, 233, 253, 262, 303] [0, 13, 28, 45, 66, 70, 79, 93, 97, 132, 204, 230, 234, 254, 263, 304] [1, 14, 29, 46, 67, 71, 80, 94, 98, 133, 205, 231, 235, 255, 264, 305] [2, 15, 30, 47, 68, 72, 81, 95, 99, 134, 206, 232, 236, 256, 265, 306] [3, 16, 31, 48, 69, 73, 82, 96, 100, 135, 207, 233, 237, 257, 266, 307] [4, 17, 32, 49, 70, 74, 83, 97, 101, 136, 208, 234, 238, 258, 267, 308] [5, 18, 33, 50, 71, 75, 84, 98, 102, 137, 209, 235, 239, 259, 268, 309] [6, 19, 34, 51, 72, 76, 85, 99, 103, 138, 210, 236, 240, 260, 269, 310] [7, 20, 35, 52, 73, 77, 86, 100, 104, 139, 211, 237, 241, 261, 270, 311] [8, 21, 36, 53, 74, 78, 87, 101, 105, 140, 212, 238, 242, 262, 271, 312] [9, 22, 37, 54, 75, 79, 88, 102, 106, 141, 213, 239, 243, 263, 272, 313] [10, 23, 38, 55, 76, 80, 89, 103, 107, 142, 214, 240, 244, 264, 273, 314] [11, 24, 39, 56, 77, 81, 90, 104, 108, 143, 215, 241, 245, 265, 274, 315] [12, 25, 40, 57, 78, 82, 91, 105, 109, 144, 216, 242, 246, 266, 275, 316] [13, 26, 41, 58, 79, 83, 92, 106, 110, 145, 217, 243, 247, 267, 276, 317] [14, 27, 42, 59, 80, 84, 93, 107, 111, 146, 218, 244, 248, 268, 277, 318] [15, 28, 43, 60, 81, 85, 94, 108, 112, 147, 219, 245, 249, 269, 278, 319] [16, 29, 44, 61, 82, 86, 95, 109, 113, 148, 220, 246, 250, 270, 279, 320] [17, 30, 45, 62, 83, 87, 96, 110, 114, 149, 221, 247, 251, 271, 280, 321] [18, 31, 46, 63, 84, 88, 97, 111, 115, 150, 222, 248, 252, 272, 281, 322] [19, 32, 47, 64, 85, 89, 98, 112, 116, 151, 223, 249, 253, 273, 282, 323] [20, 33, 48, 65, 86, 90, 99, 113, 117, 152, 224, 250, 254, 274, 283, 324] [21, 34, 49, 66, 87, 91, 100, 114, 118, 153, 225, 251, 255, 275, 284, 325] [22, 35, 50, 67, 88, 92, 101, 115, 119, 154, 226, 252, 256, 276, 285, 326] [23, 36, 51, 68, 89, 93, 102, 116, 120, 155, 227, 253, 257, 277, 286, 327] [24, 37, 52, 69, 90, 94, 103, 117, 121, 156, 228, 254, 258, 278, 287, 328] [25, 38, 53, 70, 91, 95, 104, 118, 122, 157, 229, 255, 259, 279, 288, 329] [26, 39, 54, 71, 92, 96, 105, 119, 123, 158, 165, 230, 256, 260, 280, 289] [27, 40, 55, 72, 93, 97, 106, 120, 124, 159, 166, 231, 257, 261, 281, 290] [28, 41, 56, 73, 94, 98, 107, 121, 125, 160, 167, 232, 258, 262, 282, 291] [29, 42, 57, 74, 95, 99, 108, 122, 126, 161, 168, 233, 259, 263, 283, 292] [30, 43, 58, 75, 96, 100, 109, 123, 127, 162, 169, 234, 260, 264, 284, 293] [31, 44, 59, 76, 97, 101, 110, 124, 128, 163, 170, 235, 261, 265, 285, 294] [32, 45, 60, 77, 98, 102, 111, 125, 129, 164, 171, 236, 262, 266, 286, 295] [0, 33, 46, 61, 78, 99, 103, 112, 126, 130, 172, 237, 263, 267, 287, 296] [1, 34, 47, 62, 79, 100, 104, 113, 127, 131, 173, 238, 264, 268, 288, 297] [2, 35, 48, 63, 80, 101, 105, 114, 128, 132, 174, 239, 265, 269, 289, 298] [3, 36, 49, 64, 81, 102, 106, 115, 129, 133, 175, 240, 266, 270, 290, 299]
H_Z (165 checks, sparse supports)
[30, 39, 59, 63, 89, 154, 196, 200, 214, 223, 227, 248, 265, 280, 293, 326] [31, 40, 60, 64, 90, 155, 197, 201, 215, 224, 228, 249, 266, 281, 294, 327] [32, 41, 61, 65, 91, 156, 198, 202, 216, 225, 229, 250, 267, 282, 295, 328] [33, 42, 62, 66, 92, 157, 199, 203, 217, 226, 230, 251, 268, 283, 296, 329] [34, 43, 63, 67, 93, 158, 165, 200, 204, 218, 227, 231, 252, 269, 284, 297] [35, 44, 64, 68, 94, 159, 166, 201, 205, 219, 228, 232, 253, 270, 285, 298] [36, 45, 65, 69, 95, 160, 167, 202, 206, 220, 229, 233, 254, 271, 286, 299] [37, 46, 66, 70, 96, 161, 168, 203, 207, 221, 230, 234, 255, 272, 287, 300] [38, 47, 67, 71, 97, 162, 169, 204, 208, 222, 231, 235, 256, 273, 288, 301] [39, 48, 68, 72, 98, 163, 170, 205, 209, 223, 232, 236, 257, 274, 289, 302] [40, 49, 69, 73, 99, 164, 171, 206, 210, 224, 233, 237, 258, 275, 290, 303] [0, 41, 50, 70, 74, 100, 172, 207, 211, 225, 234, 238, 259, 276, 291, 304] [1, 42, 51, 71, 75, 101, 173, 208, 212, 226, 235, 239, 260, 277, 292, 305] [2, 43, 52, 72, 76, 102, 174, 209, 213, 227, 236, 240, 261, 278, 293, 306] [3, 44, 53, 73, 77, 103, 175, 210, 214, 228, 237, 241, 262, 279, 294, 307] [4, 45, 54, 74, 78, 104, 176, 211, 215, 229, 238, 242, 263, 280, 295, 308] [5, 46, 55, 75, 79, 105, 177, 212, 216, 230, 239, 243, 264, 281, 296, 309] [6, 47, 56, 76, 80, 106, 178, 213, 217, 231, 240, 244, 265, 282, 297, 310] [7, 48, 57, 77, 81, 107, 179, 214, 218, 232, 241, 245, 266, 283, 298, 311] [8, 49, 58, 78, 82, 108, 180, 215, 219, 233, 242, 246, 267, 284, 299, 312] [9, 50, 59, 79, 83, 109, 181, 216, 220, 234, 243, 247, 268, 285, 300, 313] [10, 51, 60, 80, 84, 110, 182, 217, 221, 235, 244, 248, 269, 286, 301, 314] [11, 52, 61, 81, 85, 111, 183, 218, 222, 236, 245, 249, 270, 287, 302, 315] [12, 53, 62, 82, 86, 112, 184, 219, 223, 237, 246, 250, 271, 288, 303, 316] [13, 54, 63, 83, 87, 113, 185, 220, 224, 238, 247, 251, 272, 289, 304, 317] [14, 55, 64, 84, 88, 114, 186, 221, 225, 239, 248, 252, 273, 290, 305, 318] [15, 56, 65, 85, 89, 115, 187, 222, 226, 240, 249, 253, 274, 291, 306, 319] [16, 57, 66, 86, 90, 116, 188, 223, 227, 241, 250, 254, 275, 292, 307, 320] [17, 58, 67, 87, 91, 117, 189, 224, 228, 242, 251, 255, 276, 293, 308, 321] [18, 59, 68, 88, 92, 118, 190, 225, 229, 243, 252, 256, 277, 294, 309, 322] [19, 60, 69, 89, 93, 119, 191, 226, 230, 244, 253, 257, 278, 295, 310, 323] [20, 61, 70, 90, 94, 120, 192, 227, 231, 245, 254, 258, 279, 296, 311, 324] [21, 62, 71, 91, 95, 121, 193, 228, 232, 246, 255, 259, 280, 297, 312, 325] [22, 63, 72, 92, 96, 122, 194, 229, 233, 247, 256, 260, 281, 298, 313, 326] [23, 64, 73, 93, 97, 123, 195, 230, 234, 248, 257, 261, 282, 299, 314, 327] [24, 65, 74, 94, 98, 124, 196, 231, 235, 249, 258, 262, 283, 300, 315, 328] [25, 66, 75, 95, 99, 125, 197, 232, 236, 250, 259, 263, 284, 301, 316, 329] [26, 67, 76, 96, 100, 126, 165, 198, 233, 237, 251, 260, 264, 285, 302, 317] [27, 68, 77, 97, 101, 127, 166, 199, 234, 238, 252, 261, 265, 286, 303, 318] [28, 69, 78, 98, 102, 128, 167, 200, 235, 239, 253, 262, 266, 287, 304, 319] [29, 70, 79, 99, 103, 129, 168, 201, 236, 240, 254, 263, 267, 288, 305, 320] [30, 71, 80, 100, 104, 130, 169, 202, 237, 241, 255, 264, 268, 289, 306, 321] [31, 72, 81, 101, 105, 131, 170, 203, 238, 242, 256, 265, 269, 290, 307, 322] [32, 73, 82, 102, 106, 132, 171, 204, 239, 243, 257, 266, 270, 291, 308, 323] [33, 74, 83, 103, 107, 133, 172, 205, 240, 244, 258, 267, 271, 292, 309, 324] [34, 75, 84, 104, 108, 134, 173, 206, 241, 245, 259, 268, 272, 293, 310, 325] [35, 76, 85, 105, 109, 135, 174, 207, 242, 246, 260, 269, 273, 294, 311, 326] [36, 77, 86, 106, 110, 136, 175, 208, 243, 247, 261, 270, 274, 295, 312, 327] [37, 78, 87, 107, 111, 137, 176, 209, 244, 248, 262, 271, 275, 296, 313, 328] [38, 79, 88, 108, 112, 138, 177, 210, 245, 249, 263, 272, 276, 297, 314, 329] [39, 80, 89, 109, 113, 139, 165, 178, 211, 246, 250, 264, 273, 277, 298, 315] [40, 81, 90, 110, 114, 140, 166, 179, 212, 247, 251, 265, 274, 278, 299, 316] [41, 82, 91, 111, 115, 141, 167, 180, 213, 248, 252, 266, 275, 279, 300, 317] [42, 83, 92, 112, 116, 142, 168, 181, 214, 249, 253, 267, 276, 280, 301, 318] [43, 84, 93, 113, 117, 143, 169, 182, 215, 250, 254, 268, 277, 281, 302, 319] [44, 85, 94, 114, 118, 144, 170, 183, 216, 251, 255, 269, 278, 282, 303, 320] [45, 86, 95, 115, 119, 145, 171, 184, 217, 252, 256, 270, 279, 283, 304, 321] [46, 87, 96, 116, 120, 146, 172, 185, 218, 253, 257, 271, 280, 284, 305, 322] [47, 88, 97, 117, 121, 147, 173, 186, 219, 254, 258, 272, 281, 285, 306, 323] [48, 89, 98, 118, 122, 148, 174, 187, 220, 255, 259, 273, 282, 286, 307, 324] [49, 90, 99, 119, 123, 149, 175, 188, 221, 256, 260, 274, 283, 287, 308, 325] [50, 91, 100, 120, 124, 150, 176, 189, 222, 257, 261, 275, 284, 288, 309, 326] [51, 92, 101, 121, 125, 151, 177, 190, 223, 258, 262, 276, 285, 289, 310, 327] [52, 93, 102, 122, 126, 152, 178, 191, 224, 259, 263, 277, 286, 290, 311, 328] [53, 94, 103, 123, 127, 153, 179, 192, 225, 260, 264, 278, 287, 291, 312, 329] [54, 95, 104, 124, 128, 154, 165, 180, 193, 226, 261, 265, 279, 288, 292, 313] [55, 96, 105, 125, 129, 155, 166, 181, 194, 227, 262, 266, 280, 289, 293, 314] [56, 97, 106, 126, 130, 156, 167, 182, 195, 228, 263, 267, 281, 290, 294, 315] [57, 98, 107, 127, 131, 157, 168, 183, 196, 229, 264, 268, 282, 291, 295, 316] [58, 99, 108, 128, 132, 158, 169, 184, 197, 230, 265, 269, 283, 292, 296, 317] [59, 100, 109, 129, 133, 159, 170, 185, 198, 231, 266, 270, 284, 293, 297, 318] [60, 101, 110, 130, 134, 160, 171, 186, 199, 232, 267, 271, 285, 294, 298, 319] [61, 102, 111, 131, 135, 161, 172, 187, 200, 233, 268, 272, 286, 295, 299, 320] [62, 103, 112, 132, 136, 162, 173, 188, 201, 234, 269, 273, 287, 296, 300, 321] [63, 104, 113, 133, 137, 163, 174, 189, 202, 235, 270, 274, 288, 297, 301, 322] [64, 105, 114, 134, 138, 164, 175, 190, 203, 236, 271, 275, 289, 298, 302, 323] [0, 65, 106, 115, 135, 139, 176, 191, 204, 237, 272, 276, 290, 299, 303, 324] [1, 66, 107, 116, 136, 140, 177, 192, 205, 238, 273, 277, 291, 300, 304, 325] [2, 67, 108, 117, 137, 141, 178, 193, 206, 239, 274, 278, 292, 301, 305, 326] [3, 68, 109, 118, 138, 142, 179, 194, 207, 240, 275, 279, 293, 302, 306, 327] [4, 69, 110, 119, 139, 143, 180, 195, 208, 241, 276, 280, 294, 303, 307, 328] [5, 70, 111, 120, 140, 144, 181, 196, 209, 242, 277, 281, 295, 304, 308, 329] [6, 71, 112, 121, 141, 145, 165, 182, 197, 210, 243, 278, 282, 296, 305, 309] [7, 72, 113, 122, 142, 146, 166, 183, 198, 211, 244, 279, 283, 297, 306, 310] [8, 73, 114, 123, 143, 147, 167, 184, 199, 212, 245, 280, 284, 298, 307, 311] [9, 74, 115, 124, 144, 148, 168, 185, 200, 213, 246, 281, 285, 299, 308, 312] [10, 75, 116, 125, 145, 149, 169, 186, 201, 214, 247, 282, 286, 300, 309, 313] [11, 76, 117, 126, 146, 150, 170, 187, 202, 215, 248, 283, 287, 301, 310, 314] [12, 77, 118, 127, 147, 151, 171, 188, 203, 216, 249, 284, 288, 302, 311, 315] [13, 78, 119, 128, 148, 152, 172, 189, 204, 217, 250, 285, 289, 303, 312, 316] [14, 79, 120, 129, 149, 153, 173, 190, 205, 218, 251, 286, 290, 304, 313, 317] [15, 80, 121, 130, 150, 154, 174, 191, 206, 219, 252, 287, 291, 305, 314, 318] [16, 81, 122, 131, 151, 155, 175, 192, 207, 220, 253, 288, 292, 306, 315, 319] [17, 82, 123, 132, 152, 156, 176, 193, 208, 221, 254, 289, 293, 307, 316, 320] [18, 83, 124, 133, 153, 157, 177, 194, 209, 222, 255, 290, 294, 308, 317, 321] [19, 84, 125, 134, 154, 158, 178, 195, 210, 223, 256, 291, 295, 309, 318, 322] [20, 85, 126, 135, 155, 159, 179, 196, 211, 224, 257, 292, 296, 310, 319, 323] [21, 86, 127, 136, 156, 160, 180, 197, 212, 225, 258, 293, 297, 311, 320, 324] [22, 87, 128, 137, 157, 161, 181, 198, 213, 226, 259, 294, 298, 312, 321, 325] [23, 88, 129, 138, 158, 162, 182, 199, 214, 227, 260, 295, 299, 313, 322, 326] [24, 89, 130, 139, 159, 163, 183, 200, 215, 228, 261, 296, 300, 314, 323, 327] [25, 90, 131, 140, 160, 164, 184, 201, 216, 229, 262, 297, 301, 315, 324, 328] [0, 26, 91, 132, 141, 161, 185, 202, 217, 230, 263, 298, 302, 316, 325, 329] [1, 27, 92, 133, 142, 162, 165, 186, 203, 218, 231, 264, 299, 303, 317, 326] [2, 28, 93, 134, 143, 163, 166, 187, 204, 219, 232, 265, 300, 304, 318, 327] [3, 29, 94, 135, 144, 164, 167, 188, 205, 220, 233, 266, 301, 305, 319, 328] [0, 4, 30, 95, 136, 145, 168, 189, 206, 221, 234, 267, 302, 306, 320, 329] [1, 5, 31, 96, 137, 146, 165, 169, 190, 207, 222, 235, 268, 303, 307, 321] [2, 6, 32, 97, 138, 147, 166, 170, 191, 208, 223, 236, 269, 304, 308, 322] [3, 7, 33, 98, 139, 148, 167, 171, 192, 209, 224, 237, 270, 305, 309, 323] [4, 8, 34, 99, 140, 149, 168, 172, 193, 210, 225, 238, 271, 306, 310, 324] [5, 9, 35, 100, 141, 150, 169, 173, 194, 211, 226, 239, 272, 307, 311, 325] [6, 10, 36, 101, 142, 151, 170, 174, 195, 212, 227, 240, 273, 308, 312, 326] [7, 11, 37, 102, 143, 152, 171, 175, 196, 213, 228, 241, 274, 309, 313, 327] [8, 12, 38, 103, 144, 153, 172, 176, 197, 214, 229, 242, 275, 310, 314, 328] [9, 13, 39, 104, 145, 154, 173, 177, 198, 215, 230, 243, 276, 311, 315, 329] [10, 14, 40, 105, 146, 155, 165, 174, 178, 199, 216, 231, 244, 277, 312, 316] [11, 15, 41, 106, 147, 156, 166, 175, 179, 200, 217, 232, 245, 278, 313, 317] [12, 16, 42, 107, 148, 157, 167, 176, 180, 201, 218, 233, 246, 279, 314, 318] [13, 17, 43, 108, 149, 158, 168, 177, 181, 202, 219, 234, 247, 280, 315, 319] [14, 18, 44, 109, 150, 159, 169, 178, 182, 203, 220, 235, 248, 281, 316, 320] [15, 19, 45, 110, 151, 160, 170, 179, 183, 204, 221, 236, 249, 282, 317, 321] [16, 20, 46, 111, 152, 161, 171, 180, 184, 205, 222, 237, 250, 283, 318, 322] [17, 21, 47, 112, 153, 162, 172, 181, 185, 206, 223, 238, 251, 284, 319, 323] [18, 22, 48, 113, 154, 163, 173, 182, 186, 207, 224, 239, 252, 285, 320, 324] [19, 23, 49, 114, 155, 164, 174, 183, 187, 208, 225, 240, 253, 286, 321, 325] [0, 20, 24, 50, 115, 156, 175, 184, 188, 209, 226, 241, 254, 287, 322, 326] [1, 21, 25, 51, 116, 157, 176, 185, 189, 210, 227, 242, 255, 288, 323, 327] [2, 22, 26, 52, 117, 158, 177, 186, 190, 211, 228, 243, 256, 289, 324, 328] [3, 23, 27, 53, 118, 159, 178, 187, 191, 212, 229, 244, 257, 290, 325, 329] [4, 24, 28, 54, 119, 160, 165, 179, 188, 192, 213, 230, 245, 258, 291, 326] [5, 25, 29, 55, 120, 161, 166, 180, 189, 193, 214, 231, 246, 259, 292, 327] [6, 26, 30, 56, 121, 162, 167, 181, 190, 194, 215, 232, 247, 260, 293, 328] [7, 27, 31, 57, 122, 163, 168, 182, 191, 195, 216, 233, 248, 261, 294, 329] [8, 28, 32, 58, 123, 164, 165, 169, 183, 192, 196, 217, 234, 249, 262, 295] [0, 9, 29, 33, 59, 124, 166, 170, 184, 193, 197, 218, 235, 250, 263, 296] [1, 10, 30, 34, 60, 125, 167, 171, 185, 194, 198, 219, 236, 251, 264, 297] [2, 11, 31, 35, 61, 126, 168, 172, 186, 195, 199, 220, 237, 252, 265, 298] [3, 12, 32, 36, 62, 127, 169, 173, 187, 196, 200, 221, 238, 253, 266, 299] [4, 13, 33, 37, 63, 128, 170, 174, 188, 197, 201, 222, 239, 254, 267, 300] [5, 14, 34, 38, 64, 129, 171, 175, 189, 198, 202, 223, 240, 255, 268, 301] [6, 15, 35, 39, 65, 130, 172, 176, 190, 199, 203, 224, 241, 256, 269, 302] [7, 16, 36, 40, 66, 131, 173, 177, 191, 200, 204, 225, 242, 257, 270, 303] [8, 17, 37, 41, 67, 132, 174, 178, 192, 201, 205, 226, 243, 258, 271, 304] [9, 18, 38, 42, 68, 133, 175, 179, 193, 202, 206, 227, 244, 259, 272, 305] [10, 19, 39, 43, 69, 134, 176, 180, 194, 203, 207, 228, 245, 260, 273, 306] [11, 20, 40, 44, 70, 135, 177, 181, 195, 204, 208, 229, 246, 261, 274, 307] [12, 21, 41, 45, 71, 136, 178, 182, 196, 205, 209, 230, 247, 262, 275, 308] [13, 22, 42, 46, 72, 137, 179, 183, 197, 206, 210, 231, 248, 263, 276, 309] [14, 23, 43, 47, 73, 138, 180, 184, 198, 207, 211, 232, 249, 264, 277, 310] [15, 24, 44, 48, 74, 139, 181, 185, 199, 208, 212, 233, 250, 265, 278, 311] [16, 25, 45, 49, 75, 140, 182, 186, 200, 209, 213, 234, 251, 266, 279, 312] [17, 26, 46, 50, 76, 141, 183, 187, 201, 210, 214, 235, 252, 267, 280, 313] [18, 27, 47, 51, 77, 142, 184, 188, 202, 211, 215, 236, 253, 268, 281, 314] [19, 28, 48, 52, 78, 143, 185, 189, 203, 212, 216, 237, 254, 269, 282, 315] [20, 29, 49, 53, 79, 144, 186, 190, 204, 213, 217, 238, 255, 270, 283, 316] [21, 30, 50, 54, 80, 145, 187, 191, 205, 214, 218, 239, 256, 271, 284, 317] [22, 31, 51, 55, 81, 146, 188, 192, 206, 215, 219, 240, 257, 272, 285, 318] [23, 32, 52, 56, 82, 147, 189, 193, 207, 216, 220, 241, 258, 273, 286, 319] [24, 33, 53, 57, 83, 148, 190, 194, 208, 217, 221, 242, 259, 274, 287, 320] [25, 34, 54, 58, 84, 149, 191, 195, 209, 218, 222, 243, 260, 275, 288, 321] [26, 35, 55, 59, 85, 150, 192, 196, 210, 219, 223, 244, 261, 276, 289, 322] [27, 36, 56, 60, 86, 151, 193, 197, 211, 220, 224, 245, 262, 277, 290, 323] [28, 37, 57, 61, 87, 152, 194, 198, 212, 221, 225, 246, 263, 278, 291, 324] [29, 38, 58, 62, 88, 153, 195, 199, 213, 222, 226, 247, 264, 279, 292, 325]
Code ID 330-50-30 · download JSON · raw on GitHub