Information on Result #547134
There is no linear OA(4143, 222, F4, 104) (dual of [222, 79, 105]-code), because residual code would yield OA(439, 117, S4, 26), but
- the linear programming bound shows that M ≥ 363759 748775 180038 987523 636245 734966 329724 329420 390400 / 1 130801 960300 911622 852867 106887 > 439 [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(4144, 223, F4, 105) (dual of [223, 79, 106]-code) | [i] | Truncation | |
| 2 | No linear OA(4145, 224, F4, 106) (dual of [224, 79, 107]-code) | [i] | ||
| 3 | No linear OA(4146, 225, F4, 107) (dual of [225, 79, 108]-code) | [i] | ||
| 4 | No linear OOA(4144, 222, F4, 2, 105) (dual of [(222, 2), 300, 106]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4145, 222, F4, 2, 106) (dual of [(222, 2), 299, 107]-NRT-code) | [i] | ||
| 6 | No linear OOA(4146, 222, F4, 2, 107) (dual of [(222, 2), 298, 108]-NRT-code) | [i] | ||
| 7 | No linear OOA(4143, 222, F4, 2, 104) (dual of [(222, 2), 301, 105]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4143, 222, F4, 3, 104) (dual of [(222, 3), 523, 105]-NRT-code) | [i] | ||
| 9 | No digital (39, 143, 222)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |