Information on Result #546681
There is no linear OA(3157, 207, F3, 102) (dual of [207, 50, 103]-code), because residual code would yield OA(355, 104, S3, 34), but
- the linear programming bound shows that M ≥ 156886 010858 484807 854054 378468 889712 644211 339363 001341 126789 276510 956457 437793 701769 100721 300683 454940 318668 109559 161920 994946 197728 957769 811558 637515 615510 901840 516204 119571 / 885 396566 461856 638142 869755 626651 841542 071726 372464 475427 680706 478414 432865 627906 503409 309515 904907 562198 156244 985091 365409 869297 751679 479371 690668 > 355 [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(3158, 208, F3, 103) (dual of [208, 50, 104]-code) | [i] | Truncation | |
| 2 | No linear OA(3159, 209, F3, 104) (dual of [209, 50, 105]-code) | [i] | ||
| 3 | No linear OOA(3158, 207, F3, 2, 103) (dual of [(207, 2), 256, 104]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3159, 207, F3, 2, 104) (dual of [(207, 2), 255, 105]-NRT-code) | [i] | ||
| 5 | No linear OOA(3157, 207, F3, 2, 102) (dual of [(207, 2), 257, 103]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3157, 207, F3, 3, 102) (dual of [(207, 3), 464, 103]-NRT-code) | [i] | ||
| 7 | No linear OOA(3157, 207, F3, 4, 102) (dual of [(207, 4), 671, 103]-NRT-code) | [i] | ||
| 8 | No linear OOA(3157, 207, F3, 5, 102) (dual of [(207, 5), 878, 103]-NRT-code) | [i] | ||
| 9 | No digital (55, 157, 207)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |