Information on Result #599513
There is no digital (52, 196, 264)-net over F4, because extracting embedded orthogonal array would yield linear OA(4196, 264, F4, 144) (dual of [264, 68, 145]-code), but
- residual code [i] would yield OA(452, 119, S4, 36), but
- the linear programming bound shows that M ≥ 357 859286 624924 007499 700605 808588 465393 308876 978703 840422 989308 837582 985335 138623 209171 597503 690371 497984 / 17 092119 397133 148679 798998 224288 670000 327306 475640 461791 263157 951334 577147 > 452 [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 (52, 197, 264)-net over F4 | [i] | m-Reduction | |
| 2 | No digital (52, 198, 264)-net over F4 | [i] | ||
| 3 | No digital (52, 199, 264)-net over F4 | [i] | ||