Information on Result #546708
There is no linear OA(3168, 238, F3, 108) (dual of [238, 70, 109]-code), because residual code would yield OA(360, 129, S3, 36), but
- the linear programming bound shows that M ≥ 57674 030952 697132 790443 905720 998593 802640 809223 073416 752042 279335 087414 913152 123006 212511 116738 060878 952363 485233 600133 944111 430235 072053 950893 113002 090729 866223 937816 818055 184289 707085 777963 233597 577169 260803 817190 576368 082652 855612 696795 / 1 339876 932129 028224 408704 392632 336848 871142 578105 667488 443071 923559 155669 234713 329184 080708 239053 777749 932729 763408 916509 224173 666637 726679 049194 921150 683911 451679 235756 206035 536178 033444 365876 501500 383504 368086 > 360 [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(3169, 239, F3, 109) (dual of [239, 70, 110]-code) | [i] | Truncation | |
| 2 | No linear OA(3170, 240, F3, 110) (dual of [240, 70, 111]-code) | [i] | ||
| 3 | No linear OOA(3169, 238, F3, 2, 109) (dual of [(238, 2), 307, 110]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3170, 238, F3, 2, 110) (dual of [(238, 2), 306, 111]-NRT-code) | [i] | ||
| 5 | No linear OOA(3168, 238, F3, 2, 108) (dual of [(238, 2), 308, 109]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3168, 238, F3, 3, 108) (dual of [(238, 3), 546, 109]-NRT-code) | [i] | ||
| 7 | No linear OOA(3168, 238, F3, 4, 108) (dual of [(238, 4), 784, 109]-NRT-code) | [i] | ||
| 8 | No linear OOA(3168, 238, F3, 5, 108) (dual of [(238, 5), 1022, 109]-NRT-code) | [i] | ||
| 9 | No digital (60, 168, 238)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |