Information on Result #546627
There is no linear OA(3138, 234, F3, 87) (dual of [234, 96, 88]-code), because residual code would yield OA(351, 146, S3, 29), but
- the linear programming bound shows that M ≥ 5126 774601 249175 366045 349858 741246 206423 340601 352320 / 2311 172455 881906 807675 878437 > 351 [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(3139, 235, F3, 88) (dual of [235, 96, 89]-code) | [i] | Truncation | |
| 2 | No linear OA(3140, 236, F3, 89) (dual of [236, 96, 90]-code) | [i] | ||
| 3 | No linear OOA(3139, 234, F3, 2, 88) (dual of [(234, 2), 329, 89]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3140, 234, F3, 2, 89) (dual of [(234, 2), 328, 90]-NRT-code) | [i] | ||
| 5 | No linear OOA(3138, 234, F3, 2, 87) (dual of [(234, 2), 330, 88]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3138, 234, F3, 3, 87) (dual of [(234, 3), 564, 88]-NRT-code) | [i] | ||
| 7 | No linear OOA(3138, 234, F3, 4, 87) (dual of [(234, 4), 798, 88]-NRT-code) | [i] | ||
| 8 | No linear OOA(3138, 234, F3, 5, 87) (dual of [(234, 5), 1032, 88]-NRT-code) | [i] | ||
| 9 | No digital (51, 138, 234)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |