Information on Result #1857131
There is no (19, 90)-sequence in base 5, because net from sequence would yield (19, m, 91)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (19, 269, 91)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5269, 91, S5, 3, 250), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 37424 802698 468357 446437 437882 008567 477370 362907 408201 802776 058739 133912 232942 646552 488832 565095 975591 174246 696177 772590 050454 835523 990979 934653 519785 835162 902998 263234 621845 185756 683349 609375 / 251 > 5269 [i]
- extracting embedded OOA [i] would yield OOA(5269, 91, S5, 3, 250), 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 (19, 90)-sequence in base 5 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (19, m, 90)-net in base 5 with m > ∞ | [i] | ||
| 3 | No digital (19, 90)-sequence over F5 (for arbitrarily large k) | [i] | ||
| 4 | No digital (19, m, 90)-net over F5 with m > ∞ | [i] | ||