Information on Result #546202
There is no linear OA(2136, 191, F2, 64) (dual of [191, 55, 65]-code), because residual code would yield OA(272, 126, S2, 32), but
- the linear programming bound shows that M ≥ 163 005211 721460 055257 870637 096174 404209 999872 / 34370 163308 084940 061297 > 272 [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(2137, 192, F2, 65) (dual of [192, 55, 66]-code) | [i] | Truncation | |
| 2 | No linear OOA(2137, 191, F2, 2, 65) (dual of [(191, 2), 245, 66]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2136, 191, F2, 2, 64) (dual of [(191, 2), 246, 65]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2136, 191, F2, 3, 64) (dual of [(191, 3), 437, 65]-NRT-code) | [i] | ||
| 5 | No linear OOA(2136, 191, F2, 4, 64) (dual of [(191, 4), 628, 65]-NRT-code) | [i] | ||
| 6 | No linear OOA(2136, 191, F2, 5, 64) (dual of [(191, 5), 819, 65]-NRT-code) | [i] | ||
| 7 | No linear OOA(2136, 191, F2, 6, 64) (dual of [(191, 6), 1010, 65]-NRT-code) | [i] | ||
| 8 | No linear OOA(2136, 191, F2, 7, 64) (dual of [(191, 7), 1201, 65]-NRT-code) | [i] | ||
| 9 | No linear OOA(2136, 191, F2, 8, 64) (dual of [(191, 8), 1392, 65]-NRT-code) | [i] | ||
| 10 | No digital (72, 136, 191)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |