Information on Result #1856372
There is no (33, 41)-sequence in base 2, because net from sequence would yield (33, m, 42)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (33, 202, 42)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2202, 42, S2, 5, 169), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 565 642191 579164 576990 770656 504089 236087 815453 811543 078026 084352 / 85 > 2202 [i]
- extracting embedded OOA [i] would yield OOA(2202, 42, S2, 5, 169), 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 (33, 41)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (33, m, 41)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (33, 41)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (33, m, 41)-net over F2 with m > ∞ | [i] | ||