Information on Result #546626
There is no linear OA(3137, 223, F3, 87) (dual of [223, 86, 88]-code), because residual code would yield OA(350, 135, S3, 29), but
- 1 times truncation [i] would yield OA(349, 134, S3, 28), but
- the linear programming bound shows that M ≥ 430073 037911 139946 191996 083081 250824 628251 158946 484375 / 1 673823 880993 304164 747289 137687 > 349 [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(3138, 224, F3, 88) (dual of [224, 86, 89]-code) | [i] | Truncation | |
| 2 | No linear OA(3139, 225, F3, 89) (dual of [225, 86, 90]-code) | [i] | ||
| 3 | No linear OOA(3138, 223, F3, 2, 88) (dual of [(223, 2), 308, 89]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3139, 223, F3, 2, 89) (dual of [(223, 2), 307, 90]-NRT-code) | [i] | ||
| 5 | No linear OOA(3137, 223, F3, 2, 87) (dual of [(223, 2), 309, 88]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3137, 223, F3, 3, 87) (dual of [(223, 3), 532, 88]-NRT-code) | [i] | ||
| 7 | No linear OOA(3137, 223, F3, 4, 87) (dual of [(223, 4), 755, 88]-NRT-code) | [i] | ||
| 8 | No linear OOA(3137, 223, F3, 5, 87) (dual of [(223, 5), 978, 88]-NRT-code) | [i] | ||
| 9 | No digital (50, 137, 223)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |