Information on Result #546770
There is no linear OA(3186, 205, F3, 123) (dual of [205, 19, 124]-code), because residual code would yield OA(363, 81, S3, 41), but
- the linear programming bound shows that M ≥ 645814 120288 256333 139417 572410 149042 / 494527 > 363 [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 OA(3187, 206, F3, 124) (dual of [206, 19, 125]-code) | [i] | Truncation | |
| 2 | No linear OA(3188, 207, F3, 125) (dual of [207, 19, 126]-code) | [i] | ||
| 3 | No linear OOA(3187, 205, F3, 2, 124) (dual of [(205, 2), 223, 125]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3188, 205, F3, 2, 125) (dual of [(205, 2), 222, 126]-NRT-code) | [i] | ||
| 5 | No linear OOA(3186, 205, F3, 2, 123) (dual of [(205, 2), 224, 124]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3186, 205, F3, 3, 123) (dual of [(205, 3), 429, 124]-NRT-code) | [i] | ||
| 7 | No linear OOA(3186, 205, F3, 4, 123) (dual of [(205, 4), 634, 124]-NRT-code) | [i] | ||
| 8 | No linear OOA(3186, 205, F3, 5, 123) (dual of [(205, 5), 839, 124]-NRT-code) | [i] | ||
| 9 | No digital (63, 186, 205)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |