Information on Result #3149035
There is no digital (50, 197, 226)-net over F4, because 3 times m-reduction would yield digital (50, 194, 226)-net over F4, but
- extracting embedded orthogonal array [i] would yield linear OA(4194, 226, F4, 144) (dual of [226, 32, 145]-code), but
- construction Y1 [i] would yield
- linear OA(4193, 208, F4, 144) (dual of [208, 15, 145]-code), but
- construction Y1 [i] would yield
- linear OA(4192, 200, F4, 144) (dual of [200, 8, 145]-code), but
- construction Y1 [i] would yield
- linear OA(4191, 196, F4, 144) (dual of [196, 5, 145]-code), but
- residual code [i] would yield linear OA(447, 51, F4, 36) (dual of [51, 4, 37]-code), but
- OA(48, 200, S4, 4), but
- discarding factors would yield OA(48, 121, S4, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 65704 > 48 [i]
- discarding factors would yield OA(48, 121, S4, 4), but
- linear OA(4191, 196, F4, 144) (dual of [196, 5, 145]-code), but
- construction Y1 [i] would yield
- OA(415, 208, S4, 8), but
- discarding factors would yield OA(415, 135, S4, 8), but
- the Rao or (dual) Hamming bound shows that M ≥ 1082 768311 > 415 [i]
- discarding factors would yield OA(415, 135, S4, 8), but
- linear OA(4192, 200, F4, 144) (dual of [200, 8, 145]-code), but
- construction Y1 [i] would yield
- OA(432, 226, S4, 18), but
- discarding factors would yield OA(432, 195, S4, 18), but
- the Rao or (dual) Hamming bound shows that M ≥ 18 632959 071185 877328 > 432 [i]
- discarding factors would yield OA(432, 195, S4, 18), but
- linear OA(4193, 208, F4, 144) (dual of [208, 15, 145]-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.