Information on Result #599714
There is no digital (6, 26, 64)-net over F5, because extracting embedded orthogonal array would yield linear OA(526, 64, F5, 20) (dual of [64, 38, 21]-code), but
- construction Y1 [i] would yield
- linear OA(525, 34, F5, 20) (dual of [34, 9, 21]-code), but
- residual code [i] would yield linear OA(55, 13, F5, 4) (dual of [13, 8, 5]-code), but
- “Bou†bound on codes from Brouwer’s database [i]
- residual code [i] would yield linear OA(55, 13, F5, 4) (dual of [13, 8, 5]-code), but
- linear OA(538, 64, F5, 30) (dual of [64, 26, 31]-code), but
- discarding factors / shortening the dual code would yield linear OA(538, 61, F5, 30) (dual of [61, 23, 31]-code), but
- construction Y1 [i] would yield
- linear OA(537, 43, F5, 30) (dual of [43, 6, 31]-code), but
- residual code [i] would yield linear OA(57, 12, F5, 6) (dual of [12, 5, 7]-code), but
- OA(523, 61, S5, 18), but
- the linear programming bound shows that M ≥ 6321 833259 448409 889221 191406 250000 / 502952 782605 714137 > 523 [i]
- linear OA(537, 43, F5, 30) (dual of [43, 6, 31]-code), but
- construction Y1 [i] would yield
- discarding factors / shortening the dual code would yield linear OA(538, 61, F5, 30) (dual of [61, 23, 31]-code), but
- linear OA(525, 34, F5, 20) (dual of [34, 9, 21]-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 (6, 27, 64)-net over F5 | [i] | m-Reduction | |
| 2 | No digital (6, 28, 64)-net over F5 | [i] | ||