Information on Result #546741
There is no linear OA(3177, 198, F3, 117) (dual of [198, 21, 118]-code), because residual code would yield OA(360, 80, S3, 39), but
- the linear programming bound shows that M ≥ 10299 241947 274765 323111 769912 609288 895091 / 233101 383112 > 360 [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(3178, 199, F3, 118) (dual of [199, 21, 119]-code) | [i] | Truncation | |
| 2 | No linear OA(3179, 200, F3, 119) (dual of [200, 21, 120]-code) | [i] | ||
| 3 | No linear OOA(3178, 198, F3, 2, 118) (dual of [(198, 2), 218, 119]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3179, 198, F3, 2, 119) (dual of [(198, 2), 217, 120]-NRT-code) | [i] | ||
| 5 | No linear OOA(3177, 198, F3, 2, 117) (dual of [(198, 2), 219, 118]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3177, 198, F3, 3, 117) (dual of [(198, 3), 417, 118]-NRT-code) | [i] | ||
| 7 | No linear OOA(3177, 198, F3, 4, 117) (dual of [(198, 4), 615, 118]-NRT-code) | [i] | ||
| 8 | No linear OOA(3177, 198, F3, 5, 117) (dual of [(198, 5), 813, 118]-NRT-code) | [i] | ||
| 9 | No digital (60, 177, 198)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |