Information on Result #546332
There is no linear OA(2171, 192, F2, 84) (dual of [192, 21, 85]-code), because residual code would yield OA(287, 107, S2, 42), but
- the linear programming bound shows that M ≥ 1155 305065 783002 570789 057883 799552 / 7 380945 > 287 [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(2172, 193, F2, 85) (dual of [193, 21, 86]-code) | [i] | Truncation | |
| 2 | No linear OOA(2172, 192, F2, 2, 85) (dual of [(192, 2), 212, 86]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2171, 192, F2, 2, 84) (dual of [(192, 2), 213, 85]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2171, 192, F2, 3, 84) (dual of [(192, 3), 405, 85]-NRT-code) | [i] | ||
| 5 | No linear OOA(2171, 192, F2, 4, 84) (dual of [(192, 4), 597, 85]-NRT-code) | [i] | ||
| 6 | No linear OOA(2171, 192, F2, 5, 84) (dual of [(192, 5), 789, 85]-NRT-code) | [i] | ||
| 7 | No linear OOA(2171, 192, F2, 6, 84) (dual of [(192, 6), 981, 85]-NRT-code) | [i] | ||
| 8 | No linear OOA(2171, 192, F2, 7, 84) (dual of [(192, 7), 1173, 85]-NRT-code) | [i] | ||
| 9 | No linear OOA(2171, 192, F2, 8, 84) (dual of [(192, 8), 1365, 85]-NRT-code) | [i] | ||
| 10 | No digital (87, 171, 192)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |