Information on Result #546314
There is no linear OA(2165, 183, F2, 82) (dual of [183, 18, 83]-code), because residual code would yield OA(283, 100, S2, 41), but
- 1 times truncation [i] 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(2166, 184, F2, 83) (dual of [184, 18, 84]-code) | [i] | Truncation | |
| 2 | No linear OOA(2166, 183, F2, 2, 83) (dual of [(183, 2), 200, 84]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2165, 183, F2, 2, 82) (dual of [(183, 2), 201, 83]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2165, 183, F2, 3, 82) (dual of [(183, 3), 384, 83]-NRT-code) | [i] | ||
| 5 | No linear OOA(2165, 183, F2, 4, 82) (dual of [(183, 4), 567, 83]-NRT-code) | [i] | ||
| 6 | No linear OOA(2165, 183, F2, 5, 82) (dual of [(183, 5), 750, 83]-NRT-code) | [i] | ||
| 7 | No linear OOA(2165, 183, F2, 6, 82) (dual of [(183, 6), 933, 83]-NRT-code) | [i] | ||
| 8 | No linear OOA(2165, 183, F2, 7, 82) (dual of [(183, 7), 1116, 83]-NRT-code) | [i] | ||
| 9 | No linear OOA(2165, 183, F2, 8, 82) (dual of [(183, 8), 1299, 83]-NRT-code) | [i] | ||
| 10 | No digital (83, 165, 183)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |