Information on Result #599061
There is no digital (54, 150, 223)-net over F3, because extracting embedded orthogonal array would yield linear OA(3150, 223, F3, 96) (dual of [223, 73, 97]-code), but
- residual code [i] would yield OA(354, 126, S3, 32), but
- the linear programming bound shows that M ≥ 15 551175 343489 816312 839781 958526 754046 650025 716899 066271 597025 177434 186311 225436 494080 388171 855211 042571 528095 306878 344834 964322 752687 664073 776320 / 247669 228492 701837 800287 038860 817164 439353 182480 938178 042680 577677 782903 404567 720365 536303 663330 806259 025721 550363 325847 > 354 [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 (54, 151, 223)-net over F3 | [i] | m-Reduction | |
| 2 | No digital (54, 152, 223)-net over F3 | [i] | ||