Information on Result #546878
There is no linear OA(3208, 224, F3, 138) (dual of [224, 16, 139]-code), because residual code would yield OA(370, 85, S3, 46), but
- the linear programming bound shows that M ≥ 640 504927 462165 667703 027244 227660 956271 / 192089 > 370 [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(3209, 225, F3, 139) (dual of [225, 16, 140]-code) | [i] | Truncation | |
| 2 | No linear OA(3210, 226, F3, 140) (dual of [226, 16, 141]-code) | [i] | ||
| 3 | No linear OOA(3209, 224, F3, 2, 139) (dual of [(224, 2), 239, 140]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3210, 224, F3, 2, 140) (dual of [(224, 2), 238, 141]-NRT-code) | [i] | ||
| 5 | No linear OOA(3208, 224, F3, 2, 138) (dual of [(224, 2), 240, 139]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3208, 224, F3, 3, 138) (dual of [(224, 3), 464, 139]-NRT-code) | [i] | ||
| 7 | No linear OOA(3208, 224, F3, 4, 138) (dual of [(224, 4), 688, 139]-NRT-code) | [i] | ||
| 8 | No linear OOA(3208, 224, F3, 5, 138) (dual of [(224, 5), 912, 139]-NRT-code) | [i] | ||
| 9 | No digital (70, 208, 224)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |