Information on Result #546719
There is no linear OA(3171, 223, F3, 111) (dual of [223, 52, 112]-code), because residual code would yield OA(360, 111, S3, 37), but
- the linear programming bound shows that M ≥ 123935 568792 005716 238073 093821 377566 373899 666515 891473 866546 732156 434237 662649 577761 952104 930600 687383 548328 236010 989613 216659 289681 775283 697533 382761 730971 562628 071493 118252 848986 661298 792237 / 2 651912 168878 349984 211244 004413 173913 645691 416562 954806 458129 553495 637719 806457 127468 273229 292776 586222 473938 179154 264603 376471 378754 376356 504885 590718 177008 802360 > 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(3172, 224, F3, 112) (dual of [224, 52, 113]-code) | [i] | Truncation | |
| 2 | No linear OA(3173, 225, F3, 113) (dual of [225, 52, 114]-code) | [i] | ||
| 3 | No linear OOA(3172, 223, F3, 2, 112) (dual of [(223, 2), 274, 113]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3173, 223, F3, 2, 113) (dual of [(223, 2), 273, 114]-NRT-code) | [i] | ||
| 5 | No linear OOA(3171, 223, F3, 2, 111) (dual of [(223, 2), 275, 112]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3171, 223, F3, 3, 111) (dual of [(223, 3), 498, 112]-NRT-code) | [i] | ||
| 7 | No linear OOA(3171, 223, F3, 4, 111) (dual of [(223, 4), 721, 112]-NRT-code) | [i] | ||
| 8 | No linear OOA(3171, 223, F3, 5, 111) (dual of [(223, 5), 944, 112]-NRT-code) | [i] | ||
| 9 | No digital (60, 171, 223)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |