Information on Result #546682
There is no linear OA(3158, 220, F3, 102) (dual of [220, 62, 103]-code), because residual code would yield OA(356, 117, S3, 34), but
- the linear programming bound shows that M ≥ 6 572194 410340 770230 274451 771326 497100 923623 922000 075795 128289 692486 098341 171127 246711 375119 351943 651309 763751 930468 347431 822816 020354 752566 819295 644666 929761 907332 186743 642811 447530 849961 611050 200963 934251 142751 221668 590723 / 12308 202851 555111 921783 293103 347655 939532 914017 434792 921389 913805 577111 709332 831929 188280 965469 376469 390645 081450 650558 456420 708726 187952 770175 852049 285692 893702 393942 713983 331625 662904 794533 488932 > 356 [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(3159, 221, F3, 103) (dual of [221, 62, 104]-code) | [i] | Truncation | |
| 2 | No linear OA(3160, 222, F3, 104) (dual of [222, 62, 105]-code) | [i] | ||
| 3 | No linear OOA(3159, 220, F3, 2, 103) (dual of [(220, 2), 281, 104]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3160, 220, F3, 2, 104) (dual of [(220, 2), 280, 105]-NRT-code) | [i] | ||
| 5 | No linear OOA(3158, 220, F3, 2, 102) (dual of [(220, 2), 282, 103]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3158, 220, F3, 3, 102) (dual of [(220, 3), 502, 103]-NRT-code) | [i] | ||
| 7 | No linear OOA(3158, 220, F3, 4, 102) (dual of [(220, 4), 722, 103]-NRT-code) | [i] | ||
| 8 | No linear OOA(3158, 220, F3, 5, 102) (dual of [(220, 5), 942, 103]-NRT-code) | [i] | ||
| 9 | No digital (56, 158, 220)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |