Information on Result #599038
There is no digital (51, 141, 214)-net over F3, because extracting embedded orthogonal array would yield linear OA(3141, 214, F3, 90) (dual of [214, 73, 91]-code), but
- residual code [i] would yield OA(351, 123, S3, 30), but
- the linear programming bound shows that M ≥ 184 562452 634065 452157 662353 211684 517149 197249 714498 133253 737898 233581 110360 924816 302833 420114 709971 475375 / 80 717016 244069 464587 443624 242700 434296 750214 169562 345287 177003 948378 401931 804237 > 351 [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 (51, 142, 214)-net over F3 | [i] | m-Reduction | |
| 2 | No digital (51, 143, 214)-net over F3 | [i] | ||