Information on Result #546651
There is no linear OA(3145, 166, F3, 96) (dual of [166, 21, 97]-code), because residual code would yield OA(349, 69, S3, 32), but
- the linear programming bound shows that M ≥ 216581 757923 721967 421601 778838 750385 / 815783 089121 > 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(3146, 167, F3, 97) (dual of [167, 21, 98]-code) | [i] | Truncation | |
| 2 | No linear OA(3147, 168, F3, 98) (dual of [168, 21, 99]-code) | [i] | ||
| 3 | No linear OOA(3146, 166, F3, 2, 97) (dual of [(166, 2), 186, 98]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3147, 166, F3, 2, 98) (dual of [(166, 2), 185, 99]-NRT-code) | [i] | ||
| 5 | No linear OOA(3145, 166, F3, 2, 96) (dual of [(166, 2), 187, 97]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3145, 166, F3, 3, 96) (dual of [(166, 3), 353, 97]-NRT-code) | [i] | ||
| 7 | No linear OOA(3145, 166, F3, 4, 96) (dual of [(166, 4), 519, 97]-NRT-code) | [i] | ||
| 8 | No linear OOA(3145, 166, F3, 5, 96) (dual of [(166, 5), 685, 97]-NRT-code) | [i] | ||
| 9 | No digital (49, 145, 166)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |