Information on Result #3150668
There is no digital (3, 23, 35)-net over F7, because 2 times m-reduction would yield digital (3, 21, 35)-net over F7, but
- extracting embedded orthogonal array [i] would yield linear OA(721, 35, F7, 18) (dual of [35, 14, 19]-code), but
- construction Y1 [i] would yield
- linear OA(720, 23, F7, 18) (dual of [23, 3, 19]-code), but
- “Hi4†bound on codes from Brouwer’s database [i]
- linear OA(714, 35, F7, 12) (dual of [35, 21, 13]-code), but
- discarding factors / shortening the dual code 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
- discarding factors / shortening the dual code would yield linear OA(714, 30, F7, 12) (dual of [30, 16, 13]-code), but
- linear OA(720, 23, F7, 18) (dual of [23, 3, 19]-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.