Information on Result #599504
There is no digital (51, 187, 279)-net over F4, because extracting embedded orthogonal array would yield linear OA(4187, 279, F4, 136) (dual of [279, 92, 137]-code), but
- residual code [i] would yield OA(451, 142, S4, 34), but
- the linear programming bound shows that M ≥ 4 610313 159906 926525 664341 018985 134001 002935 024516 670027 849429 695227 494400 / 872927 774153 444300 468519 384817 812962 039547 > 451 [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 (51, 188, 279)-net over F4 | [i] | m-Reduction | |
| 2 | No digital (51, 189, 279)-net over F4 | [i] | ||
| 3 | No digital (51, 190, 279)-net over F4 | [i] | ||