Information on Result #599897
There is no digital (1, 17, 48)-net over F16, because extracting embedded orthogonal array would yield linear OA(1617, 48, F16, 16) (dual of [48, 31, 17]-code), but
- dual of a near-MDS code is again a near-MDS code [i] would yield linear OA(1631, 48, F16, 30) (dual of [48, 17, 31]-code), but
- discarding factors / shortening the dual code would yield linear OA(1631, 34, F16, 30) (dual of [34, 3, 31]-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, 18, 48)-net over F16 | [i] | m-Reduction | |
| 2 | No digital (1, 19, 48)-net over F16 | [i] | ||
| 3 | No digital (1, 20, 48)-net over F16 | [i] | ||
| 4 | No digital (1, 21, 48)-net over F16 | [i] | ||
| 5 | No digital (1, 22, 48)-net over F16 | [i] | ||
| 6 | No digital (1, 23, 48)-net over F16 | [i] | ||
| 7 | No digital (1, 24, 48)-net over F16 | [i] | ||
| 8 | No digital (1, 25, 48)-net over F16 | [i] | ||
| 9 | No digital (1, 26, 48)-net over F16 | [i] | ||
| 10 | No digital (1, 27, 48)-net over F16 | [i] | ||
| 11 | No digital (1, 28, 48)-net over F16 | [i] | ||
| 12 | No digital (1, 29, 48)-net over F16 | [i] | ||
| 13 | No digital (1, 30, 48)-net over F16 | [i] | ||