Information on Result #599032
There is no digital (50, 140, 204)-net over F3, because extracting embedded orthogonal array would yield linear OA(3140, 204, F3, 90) (dual of [204, 64, 91]-code), but
- residual code [i] would yield OA(350, 113, S3, 30), but
- the linear programming bound shows that M ≥ 596 570195 583823 721692 911689 409545 159333 416347 007509 353942 840802 048696 218909 803001 021000 425338 904291 291412 200954 459797 559193 112998 126796 056497 666716 210000 / 790 509540 724661 767547 670804 913087 923304 064947 691066 061183 661201 682713 479390 203130 739891 928552 692939 503065 752658 282066 469332 139629 > 350 [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 (50, 141, 204)-net over F3 | [i] | m-Reduction | |
| 2 | No digital (50, 142, 204)-net over F3 | [i] | ||