Information on Result #547237
There is no linear OA(4189, 236, F4, 140) (dual of [236, 47, 141]-code), because residual code would yield OA(449, 95, S4, 35), but
- the linear programming bound shows that M ≥ 41192 474812 375713 789000 699456 975821 961965 744513 198426 307979 395590 830886 737800 969827 312304 732817 560215 797035 362301 689741 847926 242075 544191 768132 126714 956760 481792 / 121742 667562 520763 956640 695430 713637 859834 747719 323855 290261 057074 960416 613540 339354 221353 298210 726466 255682 521963 771033 504571 810965 > 449 [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(4190, 237, F4, 141) (dual of [237, 47, 142]-code) | [i] | Truncation | |
| 2 | No linear OA(4191, 238, F4, 142) (dual of [238, 47, 143]-code) | [i] | ||
| 3 | No linear OA(4192, 239, F4, 143) (dual of [239, 47, 144]-code) | [i] | ||
| 4 | No linear OOA(4190, 236, F4, 2, 141) (dual of [(236, 2), 282, 142]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4191, 236, F4, 2, 142) (dual of [(236, 2), 281, 143]-NRT-code) | [i] | ||
| 6 | No linear OOA(4192, 236, F4, 2, 143) (dual of [(236, 2), 280, 144]-NRT-code) | [i] | ||
| 7 | No linear OOA(4189, 236, F4, 2, 140) (dual of [(236, 2), 283, 141]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4189, 236, F4, 3, 140) (dual of [(236, 3), 519, 141]-NRT-code) | [i] | ||
| 9 | No digital (49, 189, 236)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |