Information on Result #599242
There is no digital (78, 213, 340)-net over F3, because extracting embedded orthogonal array would yield linear OA(3213, 340, F3, 135) (dual of [340, 127, 136]-code), but
- residual code [i] would yield OA(378, 204, S3, 45), but
- 3 times truncation [i] would yield OA(375, 201, S3, 42), but
- the linear programming bound shows that M ≥ 70 125936 773107 976834 379244 843784 716640 335910 577502 309916 609029 015855 123273 912868 189563 572000 000000 / 109 901819 499502 271926 662008 620205 982068 132289 165070 372767 942049 > 375 [i]
- 3 times truncation [i] would yield OA(375, 201, 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, 214, 340)-net over F3 | [i] | m-Reduction | |
| 2 | No digital (78, 215, 340)-net over F3 | [i] | ||