Information on Result #1856622
There is no (22, 54)-sequence in base 3, because net from sequence would yield (22, m, 55)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (22, 215, 55)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3215, 55, S3, 4, 193), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 537 389129 823333 586853 296080 335211 807839 299972 771156 980844 198119 163714 294704 099499 578360 467201 555655 223887 / 97 > 3215 [i]
- extracting embedded OOA [i] would yield OOA(3215, 55, S3, 4, 193), 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, 54)-sequence in base 3 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (22, m, 54)-net in base 3 with m > ∞ | [i] | ||
| 3 | No digital (22, 54)-sequence over F3 (for arbitrarily large k) | [i] | ||
| 4 | No digital (22, m, 54)-net over F3 with m > ∞ | [i] | ||