Information on Result #1856361
There is no (22, 29)-sequence in base 2, because net from sequence would yield (22, m, 30)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (22, 143, 30)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2143, 30, S2, 5, 121), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 758 225336 750041 186812 214421 270044 291203 334144 / 61 > 2143 [i]
- extracting embedded OOA [i] would yield OOA(2143, 30, S2, 5, 121), 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 (22, 29)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (22, m, 29)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (22, 29)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (22, m, 29)-net over F2 with m > ∞ | [i] | ||