Information on Result #546730
There is no linear OA(3174, 209, F3, 114) (dual of [209, 35, 115]-code), because residual code would yield OA(360, 94, S3, 38), but
- the linear programming bound shows that M ≥ 132 944288 351905 684103 161899 822708 298724 029601 023671 / 2537 510710 702022 341000 > 360 [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(3175, 210, F3, 115) (dual of [210, 35, 116]-code) | [i] | Truncation | |
| 2 | No linear OA(3176, 211, F3, 116) (dual of [211, 35, 117]-code) | [i] | ||
| 3 | No linear OOA(3175, 209, F3, 2, 115) (dual of [(209, 2), 243, 116]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3176, 209, F3, 2, 116) (dual of [(209, 2), 242, 117]-NRT-code) | [i] | ||
| 5 | No linear OOA(3174, 209, F3, 2, 114) (dual of [(209, 2), 244, 115]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3174, 209, F3, 3, 114) (dual of [(209, 3), 453, 115]-NRT-code) | [i] | ||
| 7 | No linear OOA(3174, 209, F3, 4, 114) (dual of [(209, 4), 662, 115]-NRT-code) | [i] | ||
| 8 | No linear OOA(3174, 209, F3, 5, 114) (dual of [(209, 5), 871, 115]-NRT-code) | [i] | ||
| 9 | No digital (60, 174, 209)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |