Information on Result #1856344
There is no (5, 10)-sequence in base 2, because net from sequence would yield (5, m, 11)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (5, 23, 11)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(223, 11, S2, 3, 18), but
- the linear programming bound for OOAs shows that M ≥ 1644 167168 / 183 > 223 [i]
- extracting embedded OOA [i] would yield OOA(223, 11, S2, 3, 18), 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, 10)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (5, m, 10)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (5, 10)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (5, m, 10)-net over F2 with m > ∞ | [i] | ||