Information on Result #546716
There is no linear OA(3168, 190, F3, 111) (dual of [190, 22, 112]-code), because residual code would yield OA(357, 78, S3, 37), but
- the linear programming bound shows that M ≥ 4 189427 328087 433604 993587 700284 480257 / 2119 390625 > 357 [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(3169, 191, F3, 112) (dual of [191, 22, 113]-code) | [i] | Truncation | |
| 2 | No linear OA(3170, 192, F3, 113) (dual of [192, 22, 114]-code) | [i] | ||
| 3 | No linear OOA(3169, 190, F3, 2, 112) (dual of [(190, 2), 211, 113]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3170, 190, F3, 2, 113) (dual of [(190, 2), 210, 114]-NRT-code) | [i] | ||
| 5 | No linear OOA(3168, 190, F3, 2, 111) (dual of [(190, 2), 212, 112]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3168, 190, F3, 3, 111) (dual of [(190, 3), 402, 112]-NRT-code) | [i] | ||
| 7 | No linear OOA(3168, 190, F3, 4, 111) (dual of [(190, 4), 592, 112]-NRT-code) | [i] | ||
| 8 | No linear OOA(3168, 190, F3, 5, 111) (dual of [(190, 5), 782, 112]-NRT-code) | [i] | ||
| 9 | No digital (57, 168, 190)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |