Information on Result #1856334
There is no (0, m, 51)-net in base 49 for arbitrarily large m, because m-reduction would yield (0, 2, 51)-net in base 49, but
- mutually orthogonal hypercube bound [i]
- the generalized Rao bound for nets shows that 49m ≥ 2449 > 492 [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, 50)-sequence in base 49 | [i] | Net from Sequence | |
| 2 | No (0, 0+k, 51)-net in base 49 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (0, m, 51)-net in base 49 with unbounded m | [i] | ||
| 4 | No digital (0, 0+k, 51)-net over F49 for arbitrarily large k | [i] | ||
| 5 | No digital (0, m, 51)-net over F49 with unbounded m | [i] | ||