Information on Result #548590
There is no linear OA(355, 70, F3, 36) (dual of [70, 15, 37]-code), because construction Y1 would yield
- linear OA(354, 62, F3, 36) (dual of [62, 8, 37]-code), but
- construction Y1 [i] 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
- linear OA(353, 58, F3, 36) (dual of [58, 5, 37]-code), but
- construction Y1 [i] would yield
- OA(315, 70, S3, 8), but
- the Rao or (dual) Hamming bound shows that M ≥ 15 118041 > 315 [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(355, 70, F3, 2, 36) (dual of [(70, 2), 85, 37]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(355, 70, F3, 3, 36) (dual of [(70, 3), 155, 37]-NRT-code) | [i] | ||
| 3 | No linear OOA(355, 70, F3, 4, 36) (dual of [(70, 4), 225, 37]-NRT-code) | [i] | ||
| 4 | No linear OOA(355, 70, F3, 5, 36) (dual of [(70, 5), 295, 37]-NRT-code) | [i] | ||
| 5 | No digital (19, 55, 70)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |