Information on Result #546210
There is no linear OA(2138, 185, F2, 66) (dual of [185, 47, 67]-code), because residual code would yield OA(272, 118, S2, 33), but
- 1 times truncation [i] would yield OA(271, 117, S2, 32), but
- the linear programming bound shows that M ≥ 436299 229870 540803 344540 378506 426337 722368 / 173 222223 038567 257555 > 271 [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(2139, 186, F2, 67) (dual of [186, 47, 68]-code) | [i] | Truncation | |
| 2 | No linear OOA(2139, 185, F2, 2, 67) (dual of [(185, 2), 231, 68]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2138, 185, F2, 2, 66) (dual of [(185, 2), 232, 67]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2138, 185, F2, 3, 66) (dual of [(185, 3), 417, 67]-NRT-code) | [i] | ||
| 5 | No linear OOA(2138, 185, F2, 4, 66) (dual of [(185, 4), 602, 67]-NRT-code) | [i] | ||
| 6 | No linear OOA(2138, 185, F2, 5, 66) (dual of [(185, 5), 787, 67]-NRT-code) | [i] | ||
| 7 | No linear OOA(2138, 185, F2, 6, 66) (dual of [(185, 6), 972, 67]-NRT-code) | [i] | ||
| 8 | No linear OOA(2138, 185, F2, 7, 66) (dual of [(185, 7), 1157, 67]-NRT-code) | [i] | ||
| 9 | No linear OOA(2138, 185, F2, 8, 66) (dual of [(185, 8), 1342, 67]-NRT-code) | [i] | ||
| 10 | No digital (72, 138, 185)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |