Information on Result #546721
There is no linear OA(3173, 248, F3, 111) (dual of [248, 75, 112]-code), because residual code would yield OA(362, 136, S3, 37), but
- the linear programming bound shows that M ≥ 25 107906 551961 934560 769174 614244 000286 915780 821438 335401 839731 269118 018422 936529 743703 225263 610816 590271 097423 222819 087158 969802 653064 295993 622444 421992 834724 094091 277181 403391 938201 079579 777340 758040 595510 894725 941611 026581 156837 394107 895869 075792 152530 290305 / 60 978394 122954 076492 784397 168062 353216 564275 839619 092129 650145 178598 586317 693508 759218 909634 383305 197348 832874 724604 670145 610063 425705 187278 056568 354935 117924 137745 719797 069021 950479 890815 422812 433736 033606 282594 894113 361942 802593 > 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(3174, 249, F3, 112) (dual of [249, 75, 113]-code) | [i] | Truncation | |
| 2 | No linear OA(3175, 250, F3, 113) (dual of [250, 75, 114]-code) | [i] | ||
| 3 | No linear OOA(3174, 248, F3, 2, 112) (dual of [(248, 2), 322, 113]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3175, 248, F3, 2, 113) (dual of [(248, 2), 321, 114]-NRT-code) | [i] | ||
| 5 | No linear OOA(3173, 248, F3, 2, 111) (dual of [(248, 2), 323, 112]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3173, 248, F3, 3, 111) (dual of [(248, 3), 571, 112]-NRT-code) | [i] | ||
| 7 | No linear OOA(3173, 248, F3, 4, 111) (dual of [(248, 4), 819, 112]-NRT-code) | [i] | ||
| 8 | No linear OOA(3173, 248, F3, 5, 111) (dual of [(248, 5), 1067, 112]-NRT-code) | [i] | ||
| 9 | No digital (62, 173, 248)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |