Information on Result #546707
There is no linear OA(3167, 226, F3, 108) (dual of [226, 59, 109]-code), because residual code would yield OA(359, 117, S3, 36), but
- the linear programming bound shows that M ≥ 761 727308 447698 482542 148743 230569 434155 182882 786455 076206 353848 581403 820807 661963 484751 862555 171263 099957 412829 349685 769072 084648 120157 630433 734361 323683 270259 221443 291357 973630 261156 160974 216627 852781 876417 362687 833375 760246 069924 / 51122 849719 374140 322887 143047 504511 568594 316413 366999 782333 439013 284638 072569 059057 230504 528941 253115 325619 904540 874976 816730 143273 988924 400609 746921 908790 318590 477735 687435 119706 723653 511140 691154 502149 > 359 [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(3168, 227, F3, 109) (dual of [227, 59, 110]-code) | [i] | Truncation | |
| 2 | No linear OA(3169, 228, F3, 110) (dual of [228, 59, 111]-code) | [i] | ||
| 3 | No linear OOA(3168, 226, F3, 2, 109) (dual of [(226, 2), 284, 110]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3169, 226, F3, 2, 110) (dual of [(226, 2), 283, 111]-NRT-code) | [i] | ||
| 5 | No linear OOA(3167, 226, F3, 2, 108) (dual of [(226, 2), 285, 109]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3167, 226, F3, 3, 108) (dual of [(226, 3), 511, 109]-NRT-code) | [i] | ||
| 7 | No linear OOA(3167, 226, F3, 4, 108) (dual of [(226, 4), 737, 109]-NRT-code) | [i] | ||
| 8 | No linear OOA(3167, 226, F3, 5, 108) (dual of [(226, 5), 963, 109]-NRT-code) | [i] | ||
| 9 | No digital (59, 167, 226)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |