Information on Result #599131
There is no digital (63, 174, 261)-net over F3, because extracting embedded orthogonal array would yield linear OA(3174, 261, F3, 111) (dual of [261, 87, 112]-code), but
- residual code [i] would yield OA(363, 149, S3, 37), but
- the linear programming bound shows that M ≥ 46 631470 124673 049327 400235 264470 858493 236508 054985 173899 541299 524620 475842 712041 549727 037290 684522 127992 940560 161444 675369 235323 506654 361935 251741 549444 156200 159989 526202 879027 434375 / 37 524831 135040 905996 809144 831977 213264 438373 079442 262970 729827 862827 594743 088766 089529 538795 972448 769675 682777 166896 727335 845836 387566 113951 189899 042231 > 363 [i]
Mode: Bound (linear).
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No digital (63, 175, 261)-net over F3 | [i] | m-Reduction | |
| 2 | No digital (63, 176, 261)-net over F3 | [i] | ||