Information on Result #599282
There is no digital (82, 232, 290)-net over F3, because extracting embedded orthogonal array would yield linear OA(3232, 290, F3, 150) (dual of [290, 58, 151]-code), but
- residual code [i] would yield OA(382, 139, S3, 50), but
- the linear programming bound shows that M ≥ 1587 399042 866016 986303 890803 537138 245492 206166 258555 218457 073292 762725 146456 195326 962155 694534 950498 243860 513481 979544 181045 609868 510228 655317 898137 944968 273836 801278 213469 / 1 121662 775947 035202 501592 579753 339451 946215 941077 958998 362092 006927 786507 022495 318993 197038 312138 033878 088343 981406 194796 277022 130176 > 382 [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 (82, 233, 290)-net over F3 | [i] | m-Reduction | |
| 2 | No digital (82, 234, 290)-net over F3 | [i] | ||