Information on Result #1856600
There is no (0, 4)-sequence in base 3, because net from sequence would yield (0, m, 5)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (0, 2, 5)-net in base 3, but
- mutually orthogonal hypercube bound [i]
- the generalized Rao bound for nets shows that 3m ≥ 11 > 32 [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, 4)-sequence in base 3 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (0, m, 4)-net in base 3 with m > ∞ | [i] | ||
| 3 | No digital (0, 4)-sequence over F3 (for arbitrarily large k) | [i] | ||
| 4 | No digital (0, m, 4)-net over F3 with m > ∞ | [i] | ||