Information on Result #3147139
There is no digital (12, 51, 57)-net over F4, because 3 times m-reduction would yield digital (12, 48, 57)-net over F4, but
- extracting embedded orthogonal array [i] would yield linear OA(448, 57, F4, 36) (dual of [57, 9, 37]-code), but
- construction Y1 [i] would yield
- linear OA(447, 51, F4, 36) (dual of [51, 4, 37]-code), but
- OA(49, 57, S4, 6), but
- discarding factors would yield OA(49, 40, S4, 6), but
- the Rao or (dual) Hamming bound shows that M ≥ 273901 > 49 [i]
- discarding factors would yield OA(49, 40, S4, 6), 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.