Information on Result #599751
There is no digital (30, 132, 181)-net over F5, because extracting embedded orthogonal array would yield linear OA(5132, 181, F5, 102) (dual of [181, 49, 103]-code), but
- construction Y1 [i] would yield
- OA(5131, 147, S5, 102), but
- the linear programming bound shows that M ≥ 249 236477 010921 693845 684281 987701 342304 847343 669838 056342 020625 628930 208250 721989 315934 479236 602783 203125 / 6 326951 585981 > 5131 [i]
- OA(549, 181, S5, 34), but
- discarding factors would yield OA(549, 179, S5, 34), but
- the linear programming bound shows that M ≥ 63101 461737 633561 195888 825311 804301 658299 627461 880998 569540 679454 803466 796875 / 3 393659 613629 526150 016067 267200 843099 664623 > 549 [i]
- discarding factors would yield OA(549, 179, S5, 34), but
- OA(5131, 147, S5, 102), but
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 (30, 133, 181)-net over F5 | [i] | m-Reduction | |
| 2 | No digital (30, 134, 181)-net over F5 | [i] | ||