Information on Result #547682
There is no linear OA(2117, 168, F2, 54) (dual of [168, 51, 55]-code), because construction Y1 would yield
- OA(2116, 148, S2, 54), but
- the linear programming bound shows that M ≥ 67 089316 460630 621624 223128 238837 181334 945792 / 674 571975 > 2116 [i]
- OA(251, 168, S2, 20), but
- discarding factors would yield OA(251, 159, S2, 20), but
- the Rao or (dual) Hamming bound shows that M ≥ 2282 987168 569557 > 251 [i]
- discarding factors would yield OA(251, 159, S2, 20), 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(2118, 169, F2, 55) (dual of [169, 51, 56]-code) | [i] | Truncation | |
| 2 | No linear OOA(2118, 168, F2, 2, 55) (dual of [(168, 2), 218, 56]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2117, 168, F2, 2, 54) (dual of [(168, 2), 219, 55]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2117, 168, F2, 3, 54) (dual of [(168, 3), 387, 55]-NRT-code) | [i] | ||
| 5 | No linear OOA(2117, 168, F2, 4, 54) (dual of [(168, 4), 555, 55]-NRT-code) | [i] | ||
| 6 | No linear OOA(2117, 168, F2, 5, 54) (dual of [(168, 5), 723, 55]-NRT-code) | [i] | ||
| 7 | No linear OOA(2117, 168, F2, 6, 54) (dual of [(168, 6), 891, 55]-NRT-code) | [i] | ||
| 8 | No linear OOA(2117, 168, F2, 7, 54) (dual of [(168, 7), 1059, 55]-NRT-code) | [i] | ||
| 9 | No linear OOA(2117, 168, F2, 8, 54) (dual of [(168, 8), 1227, 55]-NRT-code) | [i] | ||
| 10 | No digital (63, 117, 168)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |