Information on Result #1856376
There is no (37, 45)-sequence in base 2, because net from sequence would yield (37, m, 46)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (37, 223, 46)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2223, 46, S2, 5, 186), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2695 994666 715063 979466 701508 701963 067363 714442 254057 248110 361024 921600 / 187 > 2223 [i]
- extracting embedded OOA [i] would yield OOA(2223, 46, S2, 5, 186), 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 (37, 45)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (37, m, 45)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (37, 45)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (37, m, 45)-net over F2 with m > ∞ | [i] | ||