Information on Result #599178
There is no digital (69, 192, 272)-net over F3, because extracting embedded orthogonal array would yield linear OA(3192, 272, F3, 123) (dual of [272, 80, 124]-code), but
- residual code [i] would yield OA(369, 148, S3, 41), but
- the linear programming bound shows that M ≥ 527 199306 719658 208896 926956 753282 382996 646971 832171 070963 054553 993200 450591 441546 901893 314193 819862 337393 820880 042121 319806 301584 641161 179874 156104 581689 649391 176134 052857 781324 366344 646605 508834 699899 215817 264311 251735 859253 836529 335378 412635 390318 558435 614367 704494 364599 306652 835549 960494 874188 110220 429716 297039 302052 791960 / 583209 910875 303263 469889 088835 657357 701840 865796 306372 080734 049489 546624 098606 841917 840472 812622 828337 614372 329030 815396 391551 616892 000268 241706 596845 254335 190377 639143 384747 649704 694395 992598 657828 113373 740022 140260 871631 828732 981772 576649 955489 025913 848348 858077 645730 817239 947263 609096 272537 > 369 [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 (69, 193, 272)-net over F3 | [i] | m-Reduction | |
| 2 | No digital (69, 194, 272)-net over F3 | [i] | ||