Information on Result #2156232
There is no linear OA(264, 72, F2, 32) (dual of [72, 8, 33]-code), because adding a parity check bit would yield linear OA(265, 73, F2, 33) (dual of [73, 8, 34]-code), but
- “BJV†bound on codes from Brouwer’s database [i]
Mode: Bound (linear).
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OOA(265, 72, F2, 2, 33) (dual of [(72, 2), 79, 34]-NRT-code) | [i] | m-Reduction for OOAs | |
| 2 | No linear OOA(266, 72, F2, 2, 34) (dual of [(72, 2), 78, 35]-NRT-code) | [i] | ||
| 3 | No linear OOA(267, 72, F2, 2, 35) (dual of [(72, 2), 77, 36]-NRT-code) | [i] | ||
| 4 | No linear OOA(268, 72, F2, 2, 36) (dual of [(72, 2), 76, 37]-NRT-code) | [i] | ||
| 5 | No linear OOA(269, 72, F2, 2, 37) (dual of [(72, 2), 75, 38]-NRT-code) | [i] | ||
| 6 | No linear OOA(270, 72, F2, 2, 38) (dual of [(72, 2), 74, 39]-NRT-code) | [i] | ||
| 7 | No linear OOA(271, 72, F2, 2, 39) (dual of [(72, 2), 73, 40]-NRT-code) | [i] | ||
| 8 | No linear OOA(272, 72, F2, 2, 40) (dual of [(72, 2), 72, 41]-NRT-code) | [i] | ||
| 9 | No linear OOA(273, 72, F2, 2, 41) (dual of [(72, 2), 71, 42]-NRT-code) | [i] | ||
| 10 | No linear OOA(274, 72, F2, 2, 42) (dual of [(72, 2), 70, 43]-NRT-code) | [i] | ||
| 11 | No linear OOA(275, 72, F2, 2, 43) (dual of [(72, 2), 69, 44]-NRT-code) | [i] | ||
| 12 | No linear OOA(276, 72, F2, 2, 44) (dual of [(72, 2), 68, 45]-NRT-code) | [i] | ||
| 13 | No linear OOA(277, 72, F2, 2, 45) (dual of [(72, 2), 67, 46]-NRT-code) | [i] | ||
| 14 | No linear OOA(278, 72, F2, 2, 46) (dual of [(72, 2), 66, 47]-NRT-code) | [i] | ||
| 15 | No linear OOA(279, 72, F2, 2, 47) (dual of [(72, 2), 65, 48]-NRT-code) | [i] | ||
| 16 | No linear OOA(280, 72, F2, 2, 48) (dual of [(72, 2), 64, 49]-NRT-code) | [i] | ||
| 17 | No linear OOA(281, 72, F2, 2, 49) (dual of [(72, 2), 63, 50]-NRT-code) | [i] | ||
| 18 | No linear OOA(282, 72, F2, 2, 50) (dual of [(72, 2), 62, 51]-NRT-code) | [i] | ||
| 19 | No linear OOA(283, 72, F2, 2, 51) (dual of [(72, 2), 61, 52]-NRT-code) | [i] | ||
| 20 | No linear OOA(284, 72, F2, 2, 52) (dual of [(72, 2), 60, 53]-NRT-code) | [i] | ||
| 21 | No linear OOA(285, 72, F2, 2, 53) (dual of [(72, 2), 59, 54]-NRT-code) | [i] | ||
| 22 | No linear OOA(286, 72, F2, 2, 54) (dual of [(72, 2), 58, 55]-NRT-code) | [i] | ||
| 23 | No linear OOA(287, 72, F2, 2, 55) (dual of [(72, 2), 57, 56]-NRT-code) | [i] | ||
| 24 | No linear OOA(288, 72, F2, 2, 56) (dual of [(72, 2), 56, 57]-NRT-code) | [i] | ||
| 25 | No linear OOA(289, 72, F2, 2, 57) (dual of [(72, 2), 55, 58]-NRT-code) | [i] | ||
| 26 | No linear OOA(290, 72, F2, 2, 58) (dual of [(72, 2), 54, 59]-NRT-code) | [i] | ||
| 27 | No linear OOA(291, 72, F2, 2, 59) (dual of [(72, 2), 53, 60]-NRT-code) | [i] | ||
| 28 | No linear OOA(292, 72, F2, 2, 60) (dual of [(72, 2), 52, 61]-NRT-code) | [i] | ||
| 29 | No linear OOA(293, 72, F2, 2, 61) (dual of [(72, 2), 51, 62]-NRT-code) | [i] | ||
| 30 | No linear OOA(294, 72, F2, 2, 62) (dual of [(72, 2), 50, 63]-NRT-code) | [i] | ||
| 31 | No linear OOA(295, 72, F2, 2, 63) (dual of [(72, 2), 49, 64]-NRT-code) | [i] | ||
| 32 | No linear OOA(264, 72, F2, 2, 32) (dual of [(72, 2), 80, 33]-NRT-code) | [i] | Depth Reduction | |
| 33 | No linear OOA(264, 72, F2, 3, 32) (dual of [(72, 3), 152, 33]-NRT-code) | [i] | ||
| 34 | No linear OOA(264, 72, F2, 4, 32) (dual of [(72, 4), 224, 33]-NRT-code) | [i] | ||
| 35 | No linear OOA(264, 72, F2, 5, 32) (dual of [(72, 5), 296, 33]-NRT-code) | [i] | ||
| 36 | No linear OOA(264, 72, F2, 6, 32) (dual of [(72, 6), 368, 33]-NRT-code) | [i] | ||
| 37 | No linear OOA(264, 72, F2, 7, 32) (dual of [(72, 7), 440, 33]-NRT-code) | [i] | ||
| 38 | No linear OOA(264, 72, F2, 8, 32) (dual of [(72, 8), 512, 33]-NRT-code) | [i] | ||
| 39 | No digital (32, 64, 72)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |
| 40 | No linear OA(2128, 137, F2, 64) (dual of [137, 9, 65]-code) | [i] | Residual Code | |
| 41 | No linear OA(265, 76, F2, 32) (dual of [76, 11, 33]-code) | [i] | Construction Y1 (Bound) | |