Information on Result #547784
There is no linear OA(3135, 204, F3, 86) (dual of [204, 69, 87]-code), because construction Y1 would yield
- linear OA(3134, 166, F3, 86) (dual of [166, 32, 87]-code), but
- construction Y1 [i] would yield
- OA(3133, 150, S3, 86), but
- the linear programming bound shows that M ≥ 10206 967808 467913 747808 389212 583004 511164 705253 854573 732746 285224 754829 / 2 832691 > 3133 [i]
- OA(332, 166, S3, 16), but
- discarding factors would yield OA(332, 156, S3, 16), but
- the Rao or (dual) Hamming bound shows that M ≥ 1906 607562 901809 > 332 [i]
- discarding factors would yield OA(332, 156, S3, 16), but
- OA(3133, 150, S3, 86), but
- construction Y1 [i] would yield
- OA(369, 204, S3, 38), but
- the linear programming bound shows that M ≥ 6 710037 728131 003348 552980 099207 116544 142102 525372 997131 892145 770552 010000 / 7482 803495 454819 242924 378875 207345 317893 > 369 [i]
Mode: Bound (linear).
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OOA(3135, 204, F3, 2, 86) (dual of [(204, 2), 273, 87]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(3135, 204, F3, 3, 86) (dual of [(204, 3), 477, 87]-NRT-code) | [i] | ||
| 3 | No linear OOA(3135, 204, F3, 4, 86) (dual of [(204, 4), 681, 87]-NRT-code) | [i] | ||
| 4 | No linear OOA(3135, 204, F3, 5, 86) (dual of [(204, 5), 885, 87]-NRT-code) | [i] | ||
| 5 | No digital (49, 135, 204)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |