Information on Result #546613
There is no linear OA(3129, 227, F3, 81) (dual of [227, 98, 82]-code), because residual code would yield OA(348, 145, S3, 27), but
- the linear programming bound shows that M ≥ 1072 673873 218950 092233 712509 383389 471446 292679 / 12873 944093 167948 027789 > 348 [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(3130, 228, F3, 82) (dual of [228, 98, 83]-code) | [i] | Truncation | |
| 2 | No linear OOA(3130, 227, F3, 2, 82) (dual of [(227, 2), 324, 83]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(3131, 227, F3, 2, 83) (dual of [(227, 2), 323, 84]-NRT-code) | [i] | ||
| 4 | No linear OOA(3129, 227, F3, 2, 81) (dual of [(227, 2), 325, 82]-NRT-code) | [i] | Depth Reduction | |
| 5 | No linear OOA(3129, 227, F3, 3, 81) (dual of [(227, 3), 552, 82]-NRT-code) | [i] | ||
| 6 | No linear OOA(3129, 227, F3, 4, 81) (dual of [(227, 4), 779, 82]-NRT-code) | [i] | ||
| 7 | No linear OOA(3129, 227, F3, 5, 81) (dual of [(227, 5), 1006, 82]-NRT-code) | [i] | ||
| 8 | No digital (48, 129, 227)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |