Information on Result #599729
There is no digital (11, 56, 65)-net over F5, because extracting embedded orthogonal array would yield linear OA(556, 65, F5, 45) (dual of [65, 9, 46]-code), but
- construction Y1 [i] would yield
- linear OA(555, 59, F5, 45) (dual of [59, 4, 46]-code), but
- residual code [i] would yield linear OA(510, 13, F5, 9) (dual of [13, 3, 10]-code), but
- 1 times truncation [i] would yield linear OA(59, 12, F5, 8) (dual of [12, 3, 9]-code), but
- residual code [i] would yield linear OA(510, 13, F5, 9) (dual of [13, 3, 10]-code), but
- OA(59, 65, S5, 6), but
- discarding factors would yield OA(59, 58, S5, 6), but
- the Rao or (dual) Hamming bound shows that M ≥ 2 001465 > 59 [i]
- discarding factors would yield OA(59, 58, S5, 6), but
- linear OA(555, 59, F5, 45) (dual of [59, 4, 46]-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, 57, 65)-net over F5 | [i] | m-Reduction | |
| 2 | No digital (11, 58, 65)-net over F5 | [i] | ||