Information on Result #546856
There is no linear OA(3206, 237, F3, 135) (dual of [237, 31, 136]-code), because residual code would yield OA(371, 101, S3, 45), but
- the linear programming bound shows that M ≥ 216 926424 924730 553674 571114 916369 905530 828790 001490 300107 / 28450 931091 725033 434712 > 371 [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(3207, 238, F3, 136) (dual of [238, 31, 137]-code) | [i] | Truncation | |
| 2 | No linear OA(3208, 239, F3, 137) (dual of [239, 31, 138]-code) | [i] | ||
| 3 | No linear OOA(3207, 237, F3, 2, 136) (dual of [(237, 2), 267, 137]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3208, 237, F3, 2, 137) (dual of [(237, 2), 266, 138]-NRT-code) | [i] | ||
| 5 | No linear OOA(3206, 237, F3, 2, 135) (dual of [(237, 2), 268, 136]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3206, 237, F3, 3, 135) (dual of [(237, 3), 505, 136]-NRT-code) | [i] | ||
| 7 | No linear OOA(3206, 237, F3, 4, 135) (dual of [(237, 4), 742, 136]-NRT-code) | [i] | ||
| 8 | No linear OOA(3206, 237, F3, 5, 135) (dual of [(237, 5), 979, 136]-NRT-code) | [i] | ||
| 9 | No digital (71, 206, 237)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |