Information on Result #546683
There is no linear OA(3159, 232, F3, 102) (dual of [232, 73, 103]-code), because residual code would yield OA(357, 129, S3, 34), but
- the linear programming bound shows that M ≥ 809354 275724 755763 388392 345759 739922 797610 964396 279375 665149 044386 576230 563429 788711 154133 451299 709022 738390 856898 439717 989850 127611 596351 869114 451031 438259 777221 098329 631772 962500 / 496 565899 544592 863342 975273 469710 153169 995856 683171 150954 405859 112820 872932 367752 443426 608748 461587 519331 493689 756263 492748 867872 843898 726516 425058 229629 > 357 [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(3160, 233, F3, 103) (dual of [233, 73, 104]-code) | [i] | Truncation | |
| 2 | No linear OA(3161, 234, F3, 104) (dual of [234, 73, 105]-code) | [i] | ||
| 3 | No linear OOA(3160, 232, F3, 2, 103) (dual of [(232, 2), 304, 104]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3161, 232, F3, 2, 104) (dual of [(232, 2), 303, 105]-NRT-code) | [i] | ||
| 5 | No linear OOA(3159, 232, F3, 2, 102) (dual of [(232, 2), 305, 103]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3159, 232, F3, 3, 102) (dual of [(232, 3), 537, 103]-NRT-code) | [i] | ||
| 7 | No linear OOA(3159, 232, F3, 4, 102) (dual of [(232, 4), 769, 103]-NRT-code) | [i] | ||
| 8 | No linear OOA(3159, 232, F3, 5, 102) (dual of [(232, 5), 1001, 103]-NRT-code) | [i] | ||
| 9 | No digital (57, 159, 232)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |