Information on Result #546768
There is no linear OA(3184, 196, F3, 123) (dual of [196, 12, 124]-code), because residual code would yield OA(361, 72, S3, 41), but
- the linear programming bound shows that M ≥ 41997 386805 997720 199850 152210 995911 / 228095 > 361 [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(3185, 197, F3, 124) (dual of [197, 12, 125]-code) | [i] | Truncation | |
| 2 | No linear OA(3186, 198, F3, 125) (dual of [198, 12, 126]-code) | [i] | ||
| 3 | No linear OOA(3185, 196, F3, 2, 124) (dual of [(196, 2), 207, 125]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3186, 196, F3, 2, 125) (dual of [(196, 2), 206, 126]-NRT-code) | [i] | ||
| 5 | No linear OOA(3184, 196, F3, 2, 123) (dual of [(196, 2), 208, 124]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3184, 196, F3, 3, 123) (dual of [(196, 3), 404, 124]-NRT-code) | [i] | ||
| 7 | No linear OOA(3184, 196, F3, 4, 123) (dual of [(196, 4), 600, 124]-NRT-code) | [i] | ||
| 8 | No linear OOA(3184, 196, F3, 5, 123) (dual of [(196, 5), 796, 124]-NRT-code) | [i] | ||
| 9 | No digital (61, 184, 196)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |