Information on Result #599921
There is no digital (2, 52, 78)-net over F25, because extracting embedded orthogonal array would yield linear OA(2552, 78, F25, 50) (dual of [78, 26, 51]-code), but
- residual code [i] would yield OA(252, 27, S25, 2), but
- bound for OAs with strength k = 2 [i]
- the Rao or (dual) Hamming bound shows that M ≥ 649 > 252 [i]
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, 53, 78)-net over F25 | [i] | m-Reduction | |
| 2 | No digital (2, 54, 78)-net over F25 | [i] | ||
| 3 | No digital (2, 55, 78)-net over F25 | [i] | ||
| 4 | No digital (2, 56, 78)-net over F25 | [i] | ||
| 5 | No digital (2, 57, 78)-net over F25 | [i] | ||
| 6 | No digital (2, 58, 78)-net over F25 | [i] | ||
| 7 | No digital (2, 59, 78)-net over F25 | [i] | ||
| 8 | No digital (2, 60, 78)-net over F25 | [i] | ||
| 9 | No digital (2, 61, 78)-net over F25 | [i] | ||
| 10 | No digital (2, 62, 78)-net over F25 | [i] | ||
| 11 | No digital (2, 63, 78)-net over F25 | [i] | ||
| 12 | No digital (2, 64, 78)-net over F25 | [i] | ||
| 13 | No digital (2, 65, 78)-net over F25 | [i] | ||
| 14 | No digital (2, 66, 78)-net over F25 | [i] | ||
| 15 | No digital (2, 67, 78)-net over F25 | [i] | ||
| 16 | No digital (2, 68, 78)-net over F25 | [i] | ||