Information on Result #3145384
There is no digital (56, 172, 179)-net over F3, because 2 times m-reduction would yield digital (56, 170, 179)-net over F3, but
- extracting embedded orthogonal array [i] would yield linear OA(3170, 179, F3, 114) (dual of [179, 9, 115]-code), but
- construction Y1 [i] would yield
- linear OA(3169, 175, F3, 114) (dual of [175, 6, 115]-code), but
- residual code [i] would yield linear OA(355, 60, F3, 38) (dual of [60, 5, 39]-code), but
- 2 times truncation [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
- 2 times truncation [i] would yield linear OA(353, 58, F3, 36) (dual of [58, 5, 37]-code), but
- residual code [i] would yield linear OA(355, 60, F3, 38) (dual of [60, 5, 39]-code), but
- OA(39, 179, 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(3169, 175, F3, 114) (dual of [175, 6, 115]-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.