Information on Result #599083
There is no digital (57, 159, 232)-net over F3, because extracting embedded orthogonal array would yield linear OA(3159, 232, F3, 102) (dual of [232, 73, 103]-code), but
- residual code [i] would yield OA(357, 129, S3, 34), but
- the linear programming bound shows that M ≥ 809354 275724 755763 388392 345759 739922 797610 964396 279375 665149 044386 576230 563429 788711 154133 451299 709022 738390 856898 439717 989850 127611 596351 869114 451031 438259 777221 098329 631772 962500 / 496 565899 544592 863342 975273 469710 153169 995856 683171 150954 405859 112820 872932 367752 443426 608748 461587 519331 493689 756263 492748 867872 843898 726516 425058 229629 > 357 [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 (57, 160, 232)-net over F3 | [i] | m-Reduction | |
| 2 | No digital (57, 161, 232)-net over F3 | [i] | ||