Information on Result #546709
There is no linear OA(3169, 251, F3, 108) (dual of [251, 82, 109]-code), because residual code would yield OA(361, 142, S3, 36), but
- the linear programming bound shows that M ≥ 110057 996992 264008 335718 129149 812789 167410 382926 297281 137489 561817 954781 539797 095330 446330 796321 986335 249770 043338 391672 954660 756429 831103 370683 368332 400198 682368 203873 342849 181601 932753 536134 620000 / 801375 596792 772331 886384 195812 844385 927415 230504 801683 142250 629380 125033 284694 411117 301101 934018 200100 135754 437215 084825 133809 831804 737408 596792 027147 668977 826191 688627 > 361 [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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(3170, 252, F3, 109) (dual of [252, 82, 110]-code) | [i] | Truncation | |
| 2 | No linear OA(3171, 253, F3, 110) (dual of [253, 82, 111]-code) | [i] | ||
| 3 | No linear OOA(3170, 251, F3, 2, 109) (dual of [(251, 2), 332, 110]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3171, 251, F3, 2, 110) (dual of [(251, 2), 331, 111]-NRT-code) | [i] | ||
| 5 | No linear OOA(3169, 251, F3, 2, 108) (dual of [(251, 2), 333, 109]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3169, 251, F3, 3, 108) (dual of [(251, 3), 584, 109]-NRT-code) | [i] | ||
| 7 | No linear OOA(3169, 251, F3, 4, 108) (dual of [(251, 4), 835, 109]-NRT-code) | [i] | ||
| 8 | No linear OOA(3169, 251, F3, 5, 108) (dual of [(251, 5), 1086, 109]-NRT-code) | [i] | ||
| 9 | No digital (61, 169, 251)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |