Information on Result #546209
There is no linear OA(2137, 176, F2, 66) (dual of [176, 39, 67]-code), because residual code would yield OA(271, 109, S2, 33), but
- 1 times truncation [i] would yield OA(270, 108, S2, 32), but
- the linear programming bound shows that M ≥ 4 297708 243581 570312 211812 843520 / 3462 071301 > 270 [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(2138, 177, F2, 67) (dual of [177, 39, 68]-code) | [i] | Truncation | |
| 2 | No linear OOA(2138, 176, F2, 2, 67) (dual of [(176, 2), 214, 68]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2137, 176, F2, 2, 66) (dual of [(176, 2), 215, 67]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2137, 176, F2, 3, 66) (dual of [(176, 3), 391, 67]-NRT-code) | [i] | ||
| 5 | No linear OOA(2137, 176, F2, 4, 66) (dual of [(176, 4), 567, 67]-NRT-code) | [i] | ||
| 6 | No linear OOA(2137, 176, F2, 5, 66) (dual of [(176, 5), 743, 67]-NRT-code) | [i] | ||
| 7 | No linear OOA(2137, 176, F2, 6, 66) (dual of [(176, 6), 919, 67]-NRT-code) | [i] | ||
| 8 | No linear OOA(2137, 176, F2, 7, 66) (dual of [(176, 7), 1095, 67]-NRT-code) | [i] | ||
| 9 | No linear OOA(2137, 176, F2, 8, 66) (dual of [(176, 8), 1271, 67]-NRT-code) | [i] | ||
| 10 | No digital (71, 137, 176)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |