Information on Result #547692
There is no linear OA(2135, 158, F2, 66) (dual of [158, 23, 67]-code), because construction Y1 would yield
- OA(2134, 150, S2, 66), but
- the linear programming bound shows that M ≥ 235 377396 587616 186439 177776 455843 253082 652672 / 10387 > 2134 [i]
- OA(223, 158, S2, 8), but
- discarding factors would yield OA(223, 120, S2, 8), but
- the Rao or (dual) Hamming bound shows that M ≥ 8 502671 > 223 [i]
- discarding factors would yield OA(223, 120, S2, 8), but
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(2136, 159, F2, 67) (dual of [159, 23, 68]-code) | [i] | Truncation | |
| 2 | No linear OOA(2136, 158, F2, 2, 67) (dual of [(158, 2), 180, 68]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2135, 158, F2, 2, 66) (dual of [(158, 2), 181, 67]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2135, 158, F2, 3, 66) (dual of [(158, 3), 339, 67]-NRT-code) | [i] | ||
| 5 | No linear OOA(2135, 158, F2, 4, 66) (dual of [(158, 4), 497, 67]-NRT-code) | [i] | ||
| 6 | No linear OOA(2135, 158, F2, 5, 66) (dual of [(158, 5), 655, 67]-NRT-code) | [i] | ||
| 7 | No linear OOA(2135, 158, F2, 6, 66) (dual of [(158, 6), 813, 67]-NRT-code) | [i] | ||
| 8 | No linear OOA(2135, 158, F2, 7, 66) (dual of [(158, 7), 971, 67]-NRT-code) | [i] | ||
| 9 | No linear OOA(2135, 158, F2, 8, 66) (dual of [(158, 8), 1129, 67]-NRT-code) | [i] | ||
| 10 | No digital (69, 135, 158)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |