Information on Result #599086
There is no digital (57, 168, 190)-net over F3, because extracting embedded orthogonal array would yield linear OA(3168, 190, F3, 111) (dual of [190, 22, 112]-code), but
- residual code [i] would yield OA(357, 78, S3, 37), but
- the linear programming bound shows that M ≥ 4 189427 328087 433604 993587 700284 480257 / 2119 390625 > 357 [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 (57, 169, 190)-net over F3 | [i] | m-Reduction | |
| 2 | No digital (57, 170, 190)-net over F3 | [i] | ||