Information on Result #3150662
There is no digital (2, 15, 30)-net over F7, because 1 times m-reduction would yield digital (2, 14, 30)-net over F7, but
- extracting embedded orthogonal array [i] would yield linear OA(714, 30, F7, 12) (dual of [30, 16, 13]-code), but
- construction Y1 [i] would yield
- linear OA(713, 16, F7, 12) (dual of [16, 3, 13]-code), but
- linear OA(716, 30, F7, 14) (dual of [30, 14, 15]-code), but
- discarding factors / shortening the dual code would yield linear OA(716, 24, F7, 14) (dual of [24, 8, 15]-code), but
- residual code [i] would yield OA(72, 9, S7, 2), but
- bound for OAs with strength k = 2 [i]
- the Rao or (dual) Hamming bound shows that M ≥ 55 > 72 [i]
- residual code [i] would yield OA(72, 9, S7, 2), but
- discarding factors / shortening the dual code would yield linear OA(716, 24, F7, 14) (dual of [24, 8, 15]-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.