Information on Result #546348
There is no linear OA(2173, 191, F2, 86) (dual of [191, 18, 87]-code), because residual code would yield OA(287, 104, S2, 43), but
- 1 times truncation [i] would yield OA(286, 103, S2, 42), but
- the linear programming bound shows that M ≥ 158456 325028 528675 187087 900672 / 1705 > 286 [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(2174, 192, F2, 87) (dual of [192, 18, 88]-code) | [i] | Truncation | |
| 2 | No linear OOA(2174, 191, F2, 2, 87) (dual of [(191, 2), 208, 88]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2173, 191, F2, 2, 86) (dual of [(191, 2), 209, 87]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2173, 191, F2, 3, 86) (dual of [(191, 3), 400, 87]-NRT-code) | [i] | ||
| 5 | No linear OOA(2173, 191, F2, 4, 86) (dual of [(191, 4), 591, 87]-NRT-code) | [i] | ||
| 6 | No linear OOA(2173, 191, F2, 5, 86) (dual of [(191, 5), 782, 87]-NRT-code) | [i] | ||
| 7 | No linear OOA(2173, 191, F2, 6, 86) (dual of [(191, 6), 973, 87]-NRT-code) | [i] | ||
| 8 | No linear OOA(2173, 191, F2, 7, 86) (dual of [(191, 7), 1164, 87]-NRT-code) | [i] | ||
| 9 | No linear OOA(2173, 191, F2, 8, 86) (dual of [(191, 8), 1355, 87]-NRT-code) | [i] | ||
| 10 | No digital (87, 173, 191)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |