Information on Result #546807
There is no linear OA(3194, 209, F3, 129) (dual of [209, 15, 130]-code), because residual code would yield OA(365, 79, S3, 43), but
- the linear programming bound shows that M ≥ 172 665163 578928 812417 146840 028215 778171 / 14 734291 > 365 [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(3195, 210, F3, 130) (dual of [210, 15, 131]-code) | [i] | Truncation | |
| 2 | No linear OA(3196, 211, F3, 131) (dual of [211, 15, 132]-code) | [i] | ||
| 3 | No linear OOA(3195, 209, F3, 2, 130) (dual of [(209, 2), 223, 131]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3196, 209, F3, 2, 131) (dual of [(209, 2), 222, 132]-NRT-code) | [i] | ||
| 5 | No linear OOA(3194, 209, F3, 2, 129) (dual of [(209, 2), 224, 130]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3194, 209, F3, 3, 129) (dual of [(209, 3), 433, 130]-NRT-code) | [i] | ||
| 7 | No linear OOA(3194, 209, F3, 4, 129) (dual of [(209, 4), 642, 130]-NRT-code) | [i] | ||
| 8 | No linear OOA(3194, 209, F3, 5, 129) (dual of [(209, 5), 851, 130]-NRT-code) | [i] | ||
| 9 | No digital (65, 194, 209)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |