Information on Result #546298
There is no linear OA(2162, 180, F2, 80) (dual of [180, 18, 81]-code), because residual code would yield OA(282, 99, S2, 40), but
- the linear programming bound shows that M ≥ 9903 520314 283042 199192 993792 / 1885 > 282 [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(2163, 181, F2, 81) (dual of [181, 18, 82]-code) | [i] | Truncation | |
| 2 | No linear OOA(2163, 180, F2, 2, 81) (dual of [(180, 2), 197, 82]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2162, 180, F2, 2, 80) (dual of [(180, 2), 198, 81]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2162, 180, F2, 3, 80) (dual of [(180, 3), 378, 81]-NRT-code) | [i] | ||
| 5 | No linear OOA(2162, 180, F2, 4, 80) (dual of [(180, 4), 558, 81]-NRT-code) | [i] | ||
| 6 | No linear OOA(2162, 180, F2, 5, 80) (dual of [(180, 5), 738, 81]-NRT-code) | [i] | ||
| 7 | No linear OOA(2162, 180, F2, 6, 80) (dual of [(180, 6), 918, 81]-NRT-code) | [i] | ||
| 8 | No linear OOA(2162, 180, F2, 7, 80) (dual of [(180, 7), 1098, 81]-NRT-code) | [i] | ||
| 9 | No linear OOA(2162, 180, F2, 8, 80) (dual of [(180, 8), 1278, 81]-NRT-code) | [i] | ||
| 10 | No digital (82, 162, 180)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |