Information on Result #598517
There is no digital (11, 19, 49)-net over F2, because extracting embedded orthogonal array would yield linear OA(219, 49, F2, 8) (dual of [49, 30, 9]-code), but
- construction Y1 [i] would yield
- linear OA(218, 35, F2, 8) (dual of [35, 17, 9]-code), but
- linear OA(230, 49, F2, 14) (dual of [49, 19, 15]-code), but
- discarding factors / shortening the dual code would yield linear OA(230, 48, F2, 14) (dual of [48, 18, 15]-code), but
- adding a parity check bit [i] would yield linear OA(231, 49, F2, 15) (dual of [49, 18, 16]-code), but
- discarding factors / shortening the dual code would yield linear OA(230, 48, F2, 14) (dual of [48, 18, 15]-code), but
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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No digital (11, 20, 49)-net over F2 | [i] | m-Reduction | |