Information on Result #599031
There is no digital (50, 137, 223)-net over F3, because extracting embedded orthogonal array would yield linear OA(3137, 223, F3, 87) (dual of [223, 86, 88]-code), but
- residual code [i] would yield OA(350, 135, S3, 29), but
- 1 times truncation [i] would yield OA(349, 134, S3, 28), but
- the linear programming bound shows that M ≥ 430073 037911 139946 191996 083081 250824 628251 158946 484375 / 1 673823 880993 304164 747289 137687 > 349 [i]
- 1 times truncation [i] would yield OA(349, 134, S3, 28), 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 (50, 138, 223)-net over F3 | [i] | m-Reduction | |
| 2 | No digital (50, 139, 223)-net over F3 | [i] | ||