Information on Result #599040
There is no digital (51, 147, 188)-net over F3, because extracting embedded orthogonal array would yield linear OA(3147, 188, F3, 96) (dual of [188, 41, 97]-code), but
- residual code [i] would yield OA(351, 91, S3, 32), but
- the linear programming bound shows that M ≥ 3 796003 121606 659684 644081 485270 254802 809922 702083 145243 272087 278428 845740 570091 586803 340207 313946 354006 591960 625547 / 1 756668 470243 430645 991636 297238 233510 101788 678484 940922 765709 380449 381903 813470 038571 507115 > 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, 148, 188)-net over F3 | [i] | m-Reduction | |
| 2 | No digital (51, 149, 188)-net over F3 | [i] | ||