Information on Result #598920
There is no digital (4, 13, 19)-net over F3, because extracting embedded orthogonal array would yield linear OA(313, 19, F3, 9) (dual of [19, 6, 10]-code), but
- construction Y1 [i] would yield
- linear OA(312, 15, F3, 9) (dual of [15, 3, 10]-code), but
- OA(36, 19, S3, 4), but
- the linear programming bound shows that M ≥ 51975 / 67 > 36 [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 (4, 14, 19)-net over F3 | [i] | m-Reduction | |
| 2 | No digital (4, 15, 19)-net over F3 | [i] | ||