Information on Result #546689
There is no linear OA(3156, 164, F3, 105) (dual of [164, 8, 106]-code), because residual code would yield OA(351, 58, S3, 35), but
- the linear programming bound shows that M ≥ 2151 540269 112482 208544 436253 / 946 > 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(3157, 165, F3, 106) (dual of [165, 8, 107]-code) | [i] | Truncation | |
| 2 | No linear OA(3158, 166, F3, 107) (dual of [166, 8, 108]-code) | [i] | ||
| 3 | No linear OOA(3157, 164, F3, 2, 106) (dual of [(164, 2), 171, 107]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3158, 164, F3, 2, 107) (dual of [(164, 2), 170, 108]-NRT-code) | [i] | ||
| 5 | No linear OOA(3156, 164, F3, 2, 105) (dual of [(164, 2), 172, 106]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3156, 164, F3, 3, 105) (dual of [(164, 3), 336, 106]-NRT-code) | [i] | ||
| 7 | No linear OOA(3156, 164, F3, 4, 105) (dual of [(164, 4), 500, 106]-NRT-code) | [i] | ||
| 8 | No linear OOA(3156, 164, F3, 5, 105) (dual of [(164, 5), 664, 106]-NRT-code) | [i] | ||
| 9 | No digital (51, 156, 164)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |