Information on Result #599770
There is no digital (2, 10, 42)-net over F7, because extracting embedded orthogonal array would yield linear OA(710, 42, F7, 8) (dual of [42, 32, 9]-code), but
- construction Y1 [i] would yield
- linear OA(79, 14, F7, 8) (dual of [14, 5, 9]-code), but
- “MPa†bound on codes from Brouwer’s database [i]
- linear OA(732, 42, F7, 28) (dual of [42, 10, 29]-code), but
- discarding factors / shortening the dual code would yield linear OA(732, 38, F7, 28) (dual of [38, 6, 29]-code), but
- linear OA(79, 14, F7, 8) (dual of [14, 5, 9]-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 (2, 11, 42)-net over F7 | [i] | m-Reduction | |