Information on Result #1857268
There is no (5, 44)-sequence in base 7, because net from sequence would yield (5, m, 45)-net in base 7 for arbitrarily large m, but
- m-reduction [i] would yield (5, 86, 45)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(786, 45, S7, 2, 81), but
- the LP bound with quadratic polynomials shows that M ≥ 405 368844 447017 397144 485951 958074 725759 929366 921792 254455 742666 234993 920165 / 82 > 786 [i]
- extracting embedded OOA [i] would yield OOA(786, 45, S7, 2, 81), but
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 (5, 44)-sequence in base 7 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (5, m, 44)-net in base 7 with m > ∞ | [i] | ||
| 3 | No digital (5, 44)-sequence over F7 (for arbitrarily large k) | [i] | ||
| 4 | No digital (5, m, 44)-net over F7 with m > ∞ | [i] | ||