Information on Result #546771
There is no linear OA(3187, 213, F3, 123) (dual of [213, 26, 124]-code), because residual code would yield OA(364, 89, S3, 41), but
- the linear programming bound shows that M ≥ 270 344305 793094 767616 866429 490879 306189 053619 / 74 160889 643750 > 364 [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(3188, 214, F3, 124) (dual of [214, 26, 125]-code) | [i] | Truncation | |
| 2 | No linear OA(3189, 215, F3, 125) (dual of [215, 26, 126]-code) | [i] | ||
| 3 | No linear OOA(3188, 213, F3, 2, 124) (dual of [(213, 2), 238, 125]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3189, 213, F3, 2, 125) (dual of [(213, 2), 237, 126]-NRT-code) | [i] | ||
| 5 | No linear OOA(3187, 213, F3, 2, 123) (dual of [(213, 2), 239, 124]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3187, 213, F3, 3, 123) (dual of [(213, 3), 452, 124]-NRT-code) | [i] | ||
| 7 | No linear OOA(3187, 213, F3, 4, 123) (dual of [(213, 4), 665, 124]-NRT-code) | [i] | ||
| 8 | No linear OOA(3187, 213, F3, 5, 123) (dual of [(213, 5), 878, 124]-NRT-code) | [i] | ||
| 9 | No digital (64, 187, 213)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |