Information on Result #1858491
There is no (0, 82)-sequence in base 81, because net from sequence would yield (0, m, 83)-net in base 81 for arbitrarily large m, but
- m-reduction [i] would yield (0, 2, 83)-net in base 81, but
- mutually orthogonal hypercube bound [i]
- the generalized Rao bound for nets shows that 81m ≥ 6641 > 812 [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, 82)-sequence in base 81 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (0, m, 82)-net in base 81 with m > ∞ | [i] | ||
| 3 | No digital (0, 82)-sequence over F81 (for arbitrarily large k) | [i] | ||
| 4 | No digital (0, m, 82)-net over F81 with m > ∞ | [i] | ||