Information on Result #1856380
There is no (41, 49)-sequence in base 2, because net from sequence would yield (41, m, 50)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (41, 292, 50)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2292, 50, S2, 6, 251), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 206886 466346 471243 136639 015229 077469 481789 758731 696650 455233 014387 554350 757213 884221 751296 / 21 > 2292 [i]
- extracting embedded OOA [i] would yield OOA(2292, 50, S2, 6, 251), 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 (41, 49)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (41, m, 49)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (41, 49)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (41, m, 49)-net over F2 with m > ∞ | [i] | ||