Information on Result #546904
There is no linear OA(3211, 223, F3, 141) (dual of [223, 12, 142]-code), because residual code would yield OA(370, 81, S3, 47), but
- 1 times truncation [i] would yield OA(369, 80, S3, 46), but
- the linear programming bound shows that M ≥ 904 357542 932493 278414 499056 136998 127663 / 977647 > 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 OA(3212, 224, F3, 142) (dual of [224, 12, 143]-code) | [i] | Truncation | |
| 2 | No linear OA(3213, 225, F3, 143) (dual of [225, 12, 144]-code) | [i] | ||
| 3 | No linear OOA(3212, 223, F3, 2, 142) (dual of [(223, 2), 234, 143]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3213, 223, F3, 2, 143) (dual of [(223, 2), 233, 144]-NRT-code) | [i] | ||
| 5 | No linear OOA(3211, 223, F3, 2, 141) (dual of [(223, 2), 235, 142]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3211, 223, F3, 3, 141) (dual of [(223, 3), 458, 142]-NRT-code) | [i] | ||
| 7 | No linear OOA(3211, 223, F3, 4, 141) (dual of [(223, 4), 681, 142]-NRT-code) | [i] | ||
| 8 | No linear OOA(3211, 223, F3, 5, 141) (dual of [(223, 5), 904, 142]-NRT-code) | [i] | ||
| 9 | No digital (70, 211, 223)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |