Information on Result #546728
There is no linear OA(3172, 190, F3, 114) (dual of [190, 18, 115]-code), because residual code would yield OA(358, 75, S3, 38), but
- the linear programming bound shows that M ≥ 425880 948792 153754 309607 908493 218857 / 85 592416 > 358 [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(3173, 191, F3, 115) (dual of [191, 18, 116]-code) | [i] | Truncation | |
| 2 | No linear OA(3174, 192, F3, 116) (dual of [192, 18, 117]-code) | [i] | ||
| 3 | No linear OOA(3173, 190, F3, 2, 115) (dual of [(190, 2), 207, 116]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3174, 190, F3, 2, 116) (dual of [(190, 2), 206, 117]-NRT-code) | [i] | ||
| 5 | No linear OOA(3172, 190, F3, 2, 114) (dual of [(190, 2), 208, 115]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3172, 190, F3, 3, 114) (dual of [(190, 3), 398, 115]-NRT-code) | [i] | ||
| 7 | No linear OOA(3172, 190, F3, 4, 114) (dual of [(190, 4), 588, 115]-NRT-code) | [i] | ||
| 8 | No linear OOA(3172, 190, F3, 5, 114) (dual of [(190, 5), 778, 115]-NRT-code) | [i] | ||
| 9 | No digital (58, 172, 190)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |