Information on Result #546729
There is no linear OA(3173, 198, F3, 114) (dual of [198, 25, 115]-code), because residual code would yield OA(359, 83, S3, 38), but
- the linear programming bound shows that M ≥ 325 626781 031292 288709 976539 068217 532079 726399 / 18937 606422 109375 > 359 [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(3174, 199, F3, 115) (dual of [199, 25, 116]-code) | [i] | Truncation | |
| 2 | No linear OA(3175, 200, F3, 116) (dual of [200, 25, 117]-code) | [i] | ||
| 3 | No linear OOA(3174, 198, F3, 2, 115) (dual of [(198, 2), 222, 116]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3175, 198, F3, 2, 116) (dual of [(198, 2), 221, 117]-NRT-code) | [i] | ||
| 5 | No linear OOA(3173, 198, F3, 2, 114) (dual of [(198, 2), 223, 115]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3173, 198, F3, 3, 114) (dual of [(198, 3), 421, 115]-NRT-code) | [i] | ||
| 7 | No linear OOA(3173, 198, F3, 4, 114) (dual of [(198, 4), 619, 115]-NRT-code) | [i] | ||
| 8 | No linear OOA(3173, 198, F3, 5, 114) (dual of [(198, 5), 817, 115]-NRT-code) | [i] | ||
| 9 | No digital (59, 173, 198)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |