Information on Result #546331
There is no linear OA(2170, 188, F2, 84) (dual of [188, 18, 85]-code), because residual code 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(2171, 189, F2, 85) (dual of [189, 18, 86]-code) | [i] | Truncation | |
| 2 | No linear OOA(2171, 188, F2, 2, 85) (dual of [(188, 2), 205, 86]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2170, 188, F2, 2, 84) (dual of [(188, 2), 206, 85]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2170, 188, F2, 3, 84) (dual of [(188, 3), 394, 85]-NRT-code) | [i] | ||
| 5 | No linear OOA(2170, 188, F2, 4, 84) (dual of [(188, 4), 582, 85]-NRT-code) | [i] | ||
| 6 | No linear OOA(2170, 188, F2, 5, 84) (dual of [(188, 5), 770, 85]-NRT-code) | [i] | ||
| 7 | No linear OOA(2170, 188, F2, 6, 84) (dual of [(188, 6), 958, 85]-NRT-code) | [i] | ||
| 8 | No linear OOA(2170, 188, F2, 7, 84) (dual of [(188, 7), 1146, 85]-NRT-code) | [i] | ||
| 9 | No linear OOA(2170, 188, F2, 8, 84) (dual of [(188, 8), 1334, 85]-NRT-code) | [i] | ||
| 10 | No digital (86, 170, 188)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |