Information on Result #546684
There is no linear OA(3160, 241, F3, 102) (dual of [241, 81, 103]-code), because residual code would yield OA(358, 138, S3, 34), but
- the linear programming bound shows that M ≥ 127476 152647 109858 836964 999510 941941 258810 174509 185909 510810 236158 485486 586777 642310 167217 093997 490577 412163 979598 552712 810081 135105 109375 / 26 664339 762561 735625 225371 208573 781952 042183 497535 838408 714653 075655 100686 712415 616991 631039 991283 863425 318551 > 358 [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(3161, 242, F3, 103) (dual of [242, 81, 104]-code) | [i] | Truncation | |
| 2 | No linear OA(3162, 243, F3, 104) (dual of [243, 81, 105]-code) | [i] | ||
| 3 | No linear OOA(3161, 241, F3, 2, 103) (dual of [(241, 2), 321, 104]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3162, 241, F3, 2, 104) (dual of [(241, 2), 320, 105]-NRT-code) | [i] | ||
| 5 | No linear OOA(3160, 241, F3, 2, 102) (dual of [(241, 2), 322, 103]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3160, 241, F3, 3, 102) (dual of [(241, 3), 563, 103]-NRT-code) | [i] | ||
| 7 | No linear OOA(3160, 241, F3, 4, 102) (dual of [(241, 4), 804, 103]-NRT-code) | [i] | ||
| 8 | No linear OOA(3160, 241, F3, 5, 102) (dual of [(241, 5), 1045, 103]-NRT-code) | [i] | ||
| 9 | No digital (58, 160, 241)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |