Information on Result #546732
There is no linear OA(3176, 231, F3, 114) (dual of [231, 55, 115]-code), because residual code would yield OA(362, 116, S3, 38), but
- the linear programming bound shows that M ≥ 317 092913 237312 931682 931230 145256 164570 899902 587673 477360 155450 374311 745951 419910 738271 470469 423748 300910 047030 562003 396664 131573 530146 865080 570074 280426 363280 161136 607519 358156 864069 602113 914689 631814 295536 292125 006549 / 788 684086 910466 147153 663101 284054 314401 233497 209874 715764 965309 878045 427152 638286 586748 473290 411470 012796 262989 930842 395578 057155 975611 958381 004404 206865 549402 120881 365315 438956 013078 947317 > 362 [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(3177, 232, F3, 115) (dual of [232, 55, 116]-code) | [i] | Truncation | |
| 2 | No linear OA(3178, 233, F3, 116) (dual of [233, 55, 117]-code) | [i] | ||
| 3 | No linear OOA(3177, 231, F3, 2, 115) (dual of [(231, 2), 285, 116]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3178, 231, F3, 2, 116) (dual of [(231, 2), 284, 117]-NRT-code) | [i] | ||
| 5 | No linear OOA(3176, 231, F3, 2, 114) (dual of [(231, 2), 286, 115]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3176, 231, F3, 3, 114) (dual of [(231, 3), 517, 115]-NRT-code) | [i] | ||
| 7 | No linear OOA(3176, 231, F3, 4, 114) (dual of [(231, 4), 748, 115]-NRT-code) | [i] | ||
| 8 | No linear OOA(3176, 231, F3, 5, 114) (dual of [(231, 5), 979, 115]-NRT-code) | [i] | ||
| 9 | No digital (62, 176, 231)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |