Information on Result #1856867
There is no (16, 59)-sequence in base 4, because net from sequence would yield (16, m, 60)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (16, 176, 60)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4176, 60, S4, 3, 160), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 614623 025657 010344 174017 910292 669206 320781 752374 469911 111262 542928 393704 766293 304881 293061 389528 483334 455296 / 161 > 4176 [i]
- extracting embedded OOA [i] would yield OOA(4176, 60, S4, 3, 160), 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 (16, 59)-sequence in base 4 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (16, m, 59)-net in base 4 with m > ∞ | [i] | ||
| 3 | No digital (16, 59)-sequence over F4 (for arbitrarily large k) | [i] | ||
| 4 | No digital (16, m, 59)-net over F4 with m > ∞ | [i] | ||