Information on Result #599240
There is no digital (78, 207, 359)-net over F3, because extracting embedded orthogonal array would yield linear OA(3207, 359, F3, 129) (dual of [359, 152, 130]-code), but
- residual code [i] would yield OA(378, 229, S3, 43), but
- 1 times truncation [i] would yield OA(377, 228, S3, 42), but
- the linear programming bound shows that M ≥ 5912 215514 524704 110906 945136 883000 212719 987869 884535 855049 744419 389403 700722 336619 158801 044684 / 1072 032675 663595 149019 556086 689047 982002 296477 532875 566121 > 377 [i]
- 1 times truncation [i] would yield OA(377, 228, S3, 42), 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 (78, 208, 359)-net over F3 | [i] | m-Reduction | |
| 2 | No digital (78, 209, 359)-net over F3 | [i] | ||