Information on Result #548589
There is no linear OA(354, 62, F3, 36) (dual of [62, 8, 37]-code), because construction Y1 would yield
- linear OA(353, 58, F3, 36) (dual of [58, 5, 37]-code), but
- residual code [i] would yield linear OA(317, 21, F3, 12) (dual of [21, 4, 13]-code), but
- OA(38, 62, S3, 4), but
- discarding factors would yield OA(38, 58, S3, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 6729 > 38 [i]
- discarding factors would yield OA(38, 58, S3, 4), but
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 OA(355, 63, F3, 37) (dual of [63, 8, 38]-code) | [i] | Truncation | |
| 2 | No linear OA(356, 64, F3, 38) (dual of [64, 8, 39]-code) | [i] | ||
| 3 | No linear OOA(355, 62, F3, 2, 37) (dual of [(62, 2), 69, 38]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(356, 62, F3, 2, 38) (dual of [(62, 2), 68, 39]-NRT-code) | [i] | ||
| 5 | No linear OOA(358, 62, F3, 2, 40) (dual of [(62, 2), 66, 41]-NRT-code) | [i] | ||
| 6 | No linear OOA(359, 62, F3, 2, 41) (dual of [(62, 2), 65, 42]-NRT-code) | [i] | ||
| 7 | No linear OOA(360, 62, F3, 2, 42) (dual of [(62, 2), 64, 43]-NRT-code) | [i] | ||
| 8 | No linear OOA(361, 62, F3, 2, 43) (dual of [(62, 2), 63, 44]-NRT-code) | [i] | ||
| 9 | No linear OOA(362, 62, F3, 2, 44) (dual of [(62, 2), 62, 45]-NRT-code) | [i] | ||
| 10 | No linear OOA(363, 62, F3, 2, 45) (dual of [(62, 2), 61, 46]-NRT-code) | [i] | ||
| 11 | No linear OOA(364, 62, F3, 2, 46) (dual of [(62, 2), 60, 47]-NRT-code) | [i] | ||
| 12 | No linear OOA(365, 62, F3, 2, 47) (dual of [(62, 2), 59, 48]-NRT-code) | [i] | ||
| 13 | No linear OOA(366, 62, F3, 2, 48) (dual of [(62, 2), 58, 49]-NRT-code) | [i] | ||
| 14 | No linear OOA(367, 62, F3, 2, 49) (dual of [(62, 2), 57, 50]-NRT-code) | [i] | ||
| 15 | No linear OOA(368, 62, F3, 2, 50) (dual of [(62, 2), 56, 51]-NRT-code) | [i] | ||
| 16 | No linear OOA(369, 62, F3, 2, 51) (dual of [(62, 2), 55, 52]-NRT-code) | [i] | ||
| 17 | No linear OOA(370, 62, F3, 2, 52) (dual of [(62, 2), 54, 53]-NRT-code) | [i] | ||
| 18 | No linear OOA(371, 62, F3, 2, 53) (dual of [(62, 2), 53, 54]-NRT-code) | [i] | ||
| 19 | No linear OOA(372, 62, F3, 2, 54) (dual of [(62, 2), 52, 55]-NRT-code) | [i] | ||
| 20 | No linear OOA(373, 62, F3, 2, 55) (dual of [(62, 2), 51, 56]-NRT-code) | [i] | ||
| 21 | No linear OOA(374, 62, F3, 2, 56) (dual of [(62, 2), 50, 57]-NRT-code) | [i] | ||
| 22 | No linear OOA(375, 62, F3, 2, 57) (dual of [(62, 2), 49, 58]-NRT-code) | [i] | ||
| 23 | No linear OOA(376, 62, F3, 2, 58) (dual of [(62, 2), 48, 59]-NRT-code) | [i] | ||
| 24 | No linear OOA(377, 62, F3, 2, 59) (dual of [(62, 2), 47, 60]-NRT-code) | [i] | ||
| 25 | No linear OOA(378, 62, F3, 2, 60) (dual of [(62, 2), 46, 61]-NRT-code) | [i] | ||
| 26 | No linear OOA(379, 62, F3, 2, 61) (dual of [(62, 2), 45, 62]-NRT-code) | [i] | ||
| 27 | No linear OOA(380, 62, F3, 2, 62) (dual of [(62, 2), 44, 63]-NRT-code) | [i] | ||
| 28 | No linear OOA(381, 62, F3, 2, 63) (dual of [(62, 2), 43, 64]-NRT-code) | [i] | ||
| 29 | No linear OOA(382, 62, F3, 2, 64) (dual of [(62, 2), 42, 65]-NRT-code) | [i] | ||
| 30 | No linear OOA(383, 62, F3, 2, 65) (dual of [(62, 2), 41, 66]-NRT-code) | [i] | ||
| 31 | No linear OOA(384, 62, F3, 2, 66) (dual of [(62, 2), 40, 67]-NRT-code) | [i] | ||
| 32 | No linear OOA(385, 62, F3, 2, 67) (dual of [(62, 2), 39, 68]-NRT-code) | [i] | ||
| 33 | No linear OOA(386, 62, F3, 2, 68) (dual of [(62, 2), 38, 69]-NRT-code) | [i] | ||
| 34 | No linear OOA(387, 62, F3, 2, 69) (dual of [(62, 2), 37, 70]-NRT-code) | [i] | ||
| 35 | No linear OOA(388, 62, F3, 2, 70) (dual of [(62, 2), 36, 71]-NRT-code) | [i] | ||
| 36 | No linear OOA(389, 62, F3, 2, 71) (dual of [(62, 2), 35, 72]-NRT-code) | [i] | ||
| 37 | No linear OOA(390, 62, F3, 2, 72) (dual of [(62, 2), 34, 73]-NRT-code) | [i] | ||
| 38 | No linear OOA(391, 62, F3, 2, 73) (dual of [(62, 2), 33, 74]-NRT-code) | [i] | ||
| 39 | No linear OOA(392, 62, F3, 2, 74) (dual of [(62, 2), 32, 75]-NRT-code) | [i] | ||
| 40 | No linear OOA(393, 62, F3, 2, 75) (dual of [(62, 2), 31, 76]-NRT-code) | [i] | ||
| 41 | No linear OOA(394, 62, F3, 2, 76) (dual of [(62, 2), 30, 77]-NRT-code) | [i] | ||
| 42 | No linear OOA(395, 62, F3, 2, 77) (dual of [(62, 2), 29, 78]-NRT-code) | [i] | ||
| 43 | No linear OOA(354, 62, F3, 2, 36) (dual of [(62, 2), 70, 37]-NRT-code) | [i] | Depth Reduction | |
| 44 | No linear OOA(354, 62, F3, 3, 36) (dual of [(62, 3), 132, 37]-NRT-code) | [i] | ||
| 45 | No linear OOA(354, 62, F3, 4, 36) (dual of [(62, 4), 194, 37]-NRT-code) | [i] | ||
| 46 | No linear OOA(354, 62, F3, 5, 36) (dual of [(62, 5), 256, 37]-NRT-code) | [i] | ||
| 47 | No digital (18, 54, 62)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |
| 48 | No linear OA(355, 70, F3, 36) (dual of [70, 15, 37]-code) | [i] | Construction Y1 (Bound) | |