Information on Result #599677
There is no digital (70, 258, 365)-net over F4, because extracting embedded orthogonal array would yield linear OA(4258, 365, F4, 188) (dual of [365, 107, 189]-code), but
- residual code [i] would yield OA(470, 176, S4, 47), but
- 1 times truncation [i] would yield OA(469, 175, S4, 46), but
- the linear programming bound shows that M ≥ 672974 508783 713085 919446 392721 434812 374063 221813 152066 788676 290147 045574 983959 198536 005103 820640 027801 847804 723200 000000 / 1 829712 211075 097010 907956 226624 270704 376891 436886 295247 592787 694007 310519 329949 > 469 [i]
- 1 times truncation [i] would yield OA(469, 175, S4, 46), 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 (70, 259, 365)-net over F4 | [i] | m-Reduction | |
| 2 | No digital (70, 260, 365)-net over F4 | [i] | ||