Information on Result #1856601
There is no (1, 7)-sequence in base 3, because net from sequence would yield (1, m, 8)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (1, 7, 8)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(37, 8, S3, 2, 6), but
- the linear programming bound for OOAs shows that M ≥ 111537 / 49 > 37 [i]
- extracting embedded OOA [i] would yield OOA(37, 8, S3, 2, 6), 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 (1, 7)-sequence in base 3 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (1, m, 7)-net in base 3 with m > ∞ | [i] | ||
| 3 | No digital (1, 7)-sequence over F3 (for arbitrarily large k) | [i] | ||
| 4 | No digital (1, m, 7)-net over F3 with m > ∞ | [i] | ||