Information on Result #546882
There is no linear OA(3212, 254, F3, 138) (dual of [254, 42, 139]-code), because residual code would yield OA(374, 115, S3, 46), but
- the linear programming bound shows that M ≥ 8 763908 391706 642886 730085 119289 615348 861817 414825 091166 679403 / 41 340331 803107 168784 037085 > 374 [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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(3213, 255, F3, 139) (dual of [255, 42, 140]-code) | [i] | Truncation | |
| 2 | No linear OA(3214, 256, F3, 140) (dual of [256, 42, 141]-code) | [i] | ||
| 3 | No linear OOA(3213, 254, F3, 2, 139) (dual of [(254, 2), 295, 140]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3214, 254, F3, 2, 140) (dual of [(254, 2), 294, 141]-NRT-code) | [i] | ||
| 5 | No linear OOA(3212, 254, F3, 2, 138) (dual of [(254, 2), 296, 139]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3212, 254, F3, 3, 138) (dual of [(254, 3), 550, 139]-NRT-code) | [i] | ||
| 7 | No linear OOA(3212, 254, F3, 4, 138) (dual of [(254, 4), 804, 139]-NRT-code) | [i] | ||
| 8 | No linear OOA(3212, 254, F3, 5, 138) (dual of [(254, 5), 1058, 139]-NRT-code) | [i] | ||
| 9 | No digital (74, 212, 254)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |