Information on Result #3150325
There is no digital (12, 68, 68)-net over F5, because 6 times m-reduction would yield digital (12, 62, 68)-net over F5, but
- extracting embedded orthogonal array [i] would yield linear OA(562, 68, F5, 50) (dual of [68, 6, 51]-code), but
- construction Y1 [i] would yield
- linear OA(561, 64, F5, 50) (dual of [64, 3, 51]-code), but
- OA(56, 68, S5, 4), but
- discarding factors would yield OA(56, 45, S5, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 16021 > 56 [i]
- discarding factors would yield OA(56, 45, S5, 4), 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.