Information on Result #599534
There is no digital (55, 207, 278)-net over F4, because extracting embedded orthogonal array would yield linear OA(4207, 278, F4, 152) (dual of [278, 71, 153]-code), but
- residual code [i] would yield OA(455, 125, S4, 38), but
- the linear programming bound shows that M ≥ 319 069835 724865 932418 074123 003651 341257 341197 442579 627763 661845 151026 883688 745199 999424 563055 993464 060641 280000 / 235791 539716 773839 952561 097991 148290 075568 550579 267395 341876 457603 747103 745171 > 455 [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 (55, 208, 278)-net over F4 | [i] | m-Reduction | |
| 2 | No digital (55, 209, 278)-net over F4 | [i] | ||
| 3 | No digital (55, 210, 278)-net over F4 | [i] | ||