Information on Result #599957
There is no digital (1, 28, 81)-net over F27, because extracting embedded orthogonal array would yield linear OA(2728, 81, F27, 27) (dual of [81, 53, 28]-code), but
- dual of a near-MDS code is again a near-MDS code [i] would yield linear OA(2753, 81, F27, 52) (dual of [81, 28, 53]-code), but
- discarding factors / shortening the dual code would yield linear OA(2753, 56, F27, 52) (dual of [56, 3, 53]-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 (1, 29, 81)-net over F27 | [i] | m-Reduction | |
| 2 | No digital (1, 30, 81)-net over F27 | [i] | ||
| 3 | No digital (1, 31, 81)-net over F27 | [i] | ||
| 4 | No digital (1, 32, 81)-net over F27 | [i] | ||
| 5 | No digital (1, 33, 81)-net over F27 | [i] | ||
| 6 | No digital (1, 34, 81)-net over F27 | [i] | ||
| 7 | No digital (1, 35, 81)-net over F27 | [i] | ||
| 8 | No digital (1, 36, 81)-net over F27 | [i] | ||
| 9 | No digital (1, 37, 81)-net over F27 | [i] | ||
| 10 | No digital (1, 38, 81)-net over F27 | [i] | ||
| 11 | No digital (1, 39, 81)-net over F27 | [i] | ||
| 12 | No digital (1, 40, 81)-net over F27 | [i] | ||
| 13 | No digital (1, 41, 81)-net over F27 | [i] | ||
| 14 | No digital (1, 42, 81)-net over F27 | [i] | ||
| 15 | No digital (1, 43, 81)-net over F27 | [i] | ||
| 16 | No digital (1, 44, 81)-net over F27 | [i] | ||
| 17 | No digital (1, 45, 81)-net over F27 | [i] | ||
| 18 | No digital (1, 46, 81)-net over F27 | [i] | ||
| 19 | No digital (1, 47, 81)-net over F27 | [i] | ||
| 20 | No digital (1, 48, 81)-net over F27 | [i] | ||
| 21 | No digital (1, 49, 81)-net over F27 | [i] | ||
| 22 | No digital (1, 50, 81)-net over F27 | [i] | ||
| 23 | No digital (1, 51, 81)-net over F27 | [i] | ||
| 24 | No digital (1, 52, 81)-net over F27 | [i] | ||