Information on Result #599506
There is no digital (51, 195, 251)-net over F4, because extracting embedded orthogonal array would yield linear OA(4195, 251, F4, 144) (dual of [251, 56, 145]-code), but
- residual code [i] would yield OA(451, 106, S4, 36), but
- the linear programming bound shows that M ≥ 907 219566 160403 704176 293457 515345 858757 089100 371311 122924 007477 969239 010740 634294 714518 600898 650465 367549 566074 081142 476796 395616 774460 995822 115648 959163 888828 416000 / 164 002267 906727 598613 394180 622318 732656 773613 528418 250949 503534 714648 038756 170225 614544 147525 285770 591818 518775 007954 617780 725292 498883 > 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, 196, 251)-net over F4 | [i] | m-Reduction | |
| 2 | No digital (51, 197, 251)-net over F4 | [i] | ||
| 3 | No digital (51, 198, 251)-net over F4 | [i] | ||