Information on Result #1858742
There is no digital (1, m, 56)-net over F27 for arbitrarily large m, because m-reduction would yield digital (1, 53, 56)-net over F27, but
- extracting embedded orthogonal array [i] would yield linear OA(2753, 56, F27, 52) (dual of [56, 3, 53]-code), but
Mode: Bound (linear).
Optimality
Show details for fixed 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 (1, 55)-sequence over F27 | [i] | Net from Sequence | |
| 2 | No digital (1, 1+k, 56)-net over F27 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No digital (1, m, 56)-net over F27 with unbounded m | [i] | ||