Information on Result #599071
There is no digital (55, 163, 177)-net over F3, because extracting embedded orthogonal array would yield linear OA(3163, 177, F3, 108) (dual of [177, 14, 109]-code), but
- construction Y1 [i] would yield
- linear OA(3162, 171, F3, 108) (dual of [171, 9, 109]-code), but
- construction Y1 [i] would yield
- linear OA(3161, 167, F3, 108) (dual of [167, 6, 109]-code), but
- residual code [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
- residual code [i] would yield linear OA(353, 58, F3, 36) (dual of [58, 5, 37]-code), but
- OA(39, 171, S3, 4), but
- discarding factors would yield OA(39, 100, S3, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 20001 > 39 [i]
- discarding factors would yield OA(39, 100, S3, 4), but
- linear OA(3161, 167, F3, 108) (dual of [167, 6, 109]-code), but
- construction Y1 [i] would yield
- OA(314, 177, S3, 6), but
- discarding factors would yield OA(314, 154, S3, 6), but
- the Rao or (dual) Hamming bound shows that M ≥ 4 822665 > 314 [i]
- discarding factors would yield OA(314, 154, S3, 6), but
- linear OA(3162, 171, F3, 108) (dual of [171, 9, 109]-code), but
Mode: Bound (linear).
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No digital (55, 164, 177)-net over F3 | [i] | m-Reduction | |
| 2 | No digital (55, 165, 177)-net over F3 | [i] | ||