Information on Result #598956
There is no digital (15, 45, 56)-net over F3, because extracting embedded orthogonal array would yield linear OA(345, 56, F3, 30) (dual of [56, 11, 31]-code), but
- construction Y1 [i] would yield
- linear OA(344, 50, F3, 30) (dual of [50, 6, 31]-code), but
- “HJL†bound on codes from Brouwer’s database [i]
- OA(311, 56, 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
- linear OA(344, 50, F3, 30) (dual of [50, 6, 31]-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
None.