Information on Result #1858399
There is no (0, 65)-sequence in base 64, because net from sequence would yield (0, m, 66)-net in base 64 for arbitrarily large m, but
- m-reduction [i] would yield (0, 2, 66)-net in base 64, but
- mutually orthogonal hypercube bound [i]
- the generalized Rao bound for nets shows that 64m ≥ 4159 > 642 [i]
Mode: Bound.
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 (0, 65)-sequence in base 64 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (0, m, 65)-net in base 64 with m > ∞ | [i] | ||
| 3 | No digital (0, 65)-sequence over F64 (for arbitrarily large k) | [i] | ||
| 4 | No digital (0, m, 65)-net over F64 with m > ∞ | [i] | ||