Information on Result #3146912
There is no digital (3, 12, 29)-net over F4, because 1 times m-reduction would yield digital (3, 11, 29)-net over F4, but
- extracting embedded orthogonal array [i] would yield linear OA(411, 29, F4, 8) (dual of [29, 18, 9]-code), but
- construction Y1 [i] would yield
- linear OA(410, 15, F4, 8) (dual of [15, 5, 9]-code), but
- residual code [i] would yield OA(42, 6, S4, 2), but
- bound for OAs with strength k = 2 [i]
- the Rao or (dual) Hamming bound shows that M ≥ 19 > 42 [i]
- residual code [i] would yield OA(42, 6, S4, 2), but
- linear OA(418, 29, F4, 14) (dual of [29, 11, 15]-code), but
- discarding factors / shortening the dual code would yield linear OA(418, 24, F4, 14) (dual of [24, 6, 15]-code), but
- “Bou†bound on codes from Brouwer’s database [i]
- discarding factors / shortening the dual code would yield linear OA(418, 24, F4, 14) (dual of [24, 6, 15]-code), but
- linear OA(410, 15, F4, 8) (dual of [15, 5, 9]-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.