Information on Result #1857269
There is no (6, 50)-sequence in base 7, because net from sequence would yield (6, m, 51)-net in base 7 for arbitrarily large m, but
- m-reduction [i] would yield (6, 99, 51)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(799, 51, S7, 2, 93), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 25 875812 076998 063930 757182 152801 734486 857625 591237 003207 471162 651133 531677 095424 480008 / 47 > 799 [i]
- extracting embedded OOA [i] would yield OOA(799, 51, S7, 2, 93), 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 (6, 50)-sequence in base 7 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (6, m, 50)-net in base 7 with m > ∞ | [i] | ||
| 3 | No digital (6, 50)-sequence over F7 (for arbitrarily large k) | [i] | ||
| 4 | No digital (6, m, 50)-net over F7 with m > ∞ | [i] | ||