Information on Result #547256
There is no linear OA(4195, 251, F4, 144) (dual of [251, 56, 145]-code), because residual code would yield OA(451, 106, S4, 36), but
- the linear programming bound shows that M ≥ 907 219566 160403 704176 293457 515345 858757 089100 371311 122924 007477 969239 010740 634294 714518 600898 650465 367549 566074 081142 476796 395616 774460 995822 115648 959163 888828 416000 / 164 002267 906727 598613 394180 622318 732656 773613 528418 250949 503534 714648 038756 170225 614544 147525 285770 591818 518775 007954 617780 725292 498883 > 451 [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(4196, 252, F4, 145) (dual of [252, 56, 146]-code) | [i] | Truncation | |
| 2 | No linear OA(4197, 253, F4, 146) (dual of [253, 56, 147]-code) | [i] | ||
| 3 | No linear OA(4198, 254, F4, 147) (dual of [254, 56, 148]-code) | [i] | ||
| 4 | No linear OOA(4196, 251, F4, 2, 145) (dual of [(251, 2), 306, 146]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4197, 251, F4, 2, 146) (dual of [(251, 2), 305, 147]-NRT-code) | [i] | ||
| 6 | No linear OOA(4198, 251, F4, 2, 147) (dual of [(251, 2), 304, 148]-NRT-code) | [i] | ||
| 7 | No linear OOA(4195, 251, F4, 2, 144) (dual of [(251, 2), 307, 145]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4195, 251, F4, 3, 144) (dual of [(251, 3), 558, 145]-NRT-code) | [i] | ||
| 9 | No digital (51, 195, 251)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |