Information on Result #599042
There is no digital (51, 153, 168)-net over F3, because extracting embedded orthogonal array would yield linear OA(3153, 168, F3, 102) (dual of [168, 15, 103]-code), but
- residual code [i] would yield OA(351, 65, S3, 34), but
- the linear programming bound shows that M ≥ 342 054256 122719 546156 841781 498869 / 115 101637 > 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, 154, 168)-net over F3 | [i] | m-Reduction | |
| 2 | No digital (51, 155, 168)-net over F3 | [i] | ||