Information on Result #546678
There is no linear OA(3154, 175, F3, 102) (dual of [175, 21, 103]-code), because residual code would yield OA(352, 72, S3, 34), but
- the linear programming bound shows that M ≥ 23373 085764 731132 483065 978750 735767 / 2987 457005 > 352 [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(3155, 176, F3, 103) (dual of [176, 21, 104]-code) | [i] | Truncation | |
| 2 | No linear OA(3156, 177, F3, 104) (dual of [177, 21, 105]-code) | [i] | ||
| 3 | No linear OOA(3155, 175, F3, 2, 103) (dual of [(175, 2), 195, 104]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3156, 175, F3, 2, 104) (dual of [(175, 2), 194, 105]-NRT-code) | [i] | ||
| 5 | No linear OOA(3154, 175, F3, 2, 102) (dual of [(175, 2), 196, 103]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3154, 175, F3, 3, 102) (dual of [(175, 3), 371, 103]-NRT-code) | [i] | ||
| 7 | No linear OOA(3154, 175, F3, 4, 102) (dual of [(175, 4), 546, 103]-NRT-code) | [i] | ||
| 8 | No linear OOA(3154, 175, F3, 5, 102) (dual of [(175, 5), 721, 103]-NRT-code) | [i] | ||
| 9 | No digital (52, 154, 175)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |