Information on Result #598953
There is no digital (14, 42, 53)-net over F3, because extracting embedded orthogonal array would yield linear OA(342, 53, F3, 28) (dual of [53, 11, 29]-code), but
- construction Y1 [i] would yield
- linear OA(341, 47, F3, 28) (dual of [47, 6, 29]-code), but
- OA(311, 53, S3, 6), but
- discarding factors would yield OA(311, 52, S3, 6), but
- the Rao or (dual) Hamming bound shows that M ≥ 182209 > 311 [i]
- discarding factors would yield OA(311, 52, S3, 6), 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 (14, 43, 53)-net over F3 | [i] | m-Reduction | |