Information on Result #1858737
There is no digital (1, m, 34)-net over F16 for arbitrarily large m, because m-reduction would yield digital (1, 31, 34)-net over F16, but
- extracting embedded orthogonal array [i] would yield linear OA(1631, 34, F16, 30) (dual of [34, 3, 31]-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, 33)-sequence over F16 | [i] | Net from Sequence | |
| 2 | No digital (1, 1+k, 34)-net over F16 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No digital (1, m, 34)-net over F16 with unbounded m | [i] | ||