Information on Result #599463
There is no digital (45, 161, 270)-net over F4, because extracting embedded orthogonal array would yield linear OA(4161, 270, F4, 116) (dual of [270, 109, 117]-code), but
- residual code [i] would yield OA(445, 153, S4, 29), but
- the linear programming bound shows that M ≥ 7517 583831 016520 242073 479093 750904 250086 178891 069652 992000 / 5 746365 386535 716878 418589 713479 > 445 [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 (45, 162, 270)-net over F4 | [i] | m-Reduction | |
| 2 | No digital (45, 163, 270)-net over F4 | [i] | ||
| 3 | No digital (45, 164, 270)-net over F4 | [i] | ||