Information on Result #3149103
There is no digital (51, 196, 251)-net over F4, because 1 times m-reduction would yield digital (51, 195, 251)-net over F4, but
- extracting embedded orthogonal array [i] 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]
- residual code [i] would yield OA(451, 106, S4, 36), 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
None.