Information on Result #1856625
There is no (25, 60)-sequence in base 3, because net from sequence would yield (25, m, 61)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (25, 239, 61)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3239, 61, S3, 4, 214), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 293 861387 637868 414683 885460 122715 934237 915947 734466 268806 770184 031747 333538 104927 216899 075611 914191 245480 963908 724891 / 215 > 3239 [i]
- extracting embedded OOA [i] would yield OOA(3239, 61, S3, 4, 214), 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 (25, 60)-sequence in base 3 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (25, m, 60)-net in base 3 with m > ∞ | [i] | ||
| 3 | No digital (25, 60)-sequence over F3 (for arbitrarily large k) | [i] | ||
| 4 | No digital (25, m, 60)-net over F3 with m > ∞ | [i] | ||