Information on Result #599473
There is no digital (46, 178, 222)-net over F4, because extracting embedded orthogonal array would yield linear OA(4178, 222, F4, 132) (dual of [222, 44, 133]-code), but
- residual code [i] would yield OA(446, 89, S4, 33), but
- the linear programming bound shows that M ≥ 159948 754090 845526 538000 065296 234178 559990 299122 417191 613523 054637 510362 523087 608926 611865 440230 434765 845983 597818 865036 995130 058350 788608 / 31 655830 017094 855639 908154 532004 566126 868766 376087 543277 919844 313859 261385 645064 532693 335140 575232 262538 565325 > 446 [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 (46, 179, 222)-net over F4 | [i] | m-Reduction | |
| 2 | No digital (46, 180, 222)-net over F4 | [i] | ||
| 3 | No digital (46, 181, 222)-net over F4 | [i] | ||