Information on Result #3143498
There is no digital (18, 61, 62)-net over F3, because 7 times m-reduction would yield digital (18, 54, 62)-net over F3, but
- extracting embedded orthogonal array [i] 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
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.