Information on Result #547494
There is no linear OA(4255, 312, F4, 188) (dual of [312, 57, 189]-code), because residual code would yield OA(467, 123, S4, 47), but
- the linear programming bound shows that M ≥ 43402 647924 975488 920450 003944 566378 964570 407885 930315 158568 274900 052775 055729 425702 074252 778284 519466 230412 079171 949623 812197 935803 959581 270319 073009 003679 424611 406027 085968 310272 / 1 972722 979992 492582 380725 903751 953752 652629 461130 906381 054114 627794 331612 476321 726116 126868 678992 555081 191829 266311 527075 509736 859232 980625 > 467 [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(4256, 313, F4, 189) (dual of [313, 57, 190]-code) | [i] | Truncation | |
| 2 | No linear OA(4257, 314, F4, 190) (dual of [314, 57, 191]-code) | [i] | ||
| 3 | No linear OA(4258, 315, F4, 191) (dual of [315, 57, 192]-code) | [i] | ||
| 4 | No linear OOA(4256, 312, F4, 2, 189) (dual of [(312, 2), 368, 190]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4257, 312, F4, 2, 190) (dual of [(312, 2), 367, 191]-NRT-code) | [i] | ||
| 6 | No linear OOA(4258, 312, F4, 2, 191) (dual of [(312, 2), 366, 192]-NRT-code) | [i] | ||
| 7 | No linear OOA(4255, 312, F4, 2, 188) (dual of [(312, 2), 369, 189]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4255, 312, F4, 3, 188) (dual of [(312, 3), 681, 189]-NRT-code) | [i] | ||
| 9 | No digital (67, 255, 312)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |