Information on Result #1857133
There is no (21, 98)-sequence in base 5, because net from sequence would yield (21, m, 99)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (21, 293, 99)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5293, 99, S5, 3, 272), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 722 618558 091825 348615 697631 773979 774645 951723 439918 975984 420030 049941 893495 036574 070926 408530 295263 375201 421734 387412 517138 317619 454518 622493 266182 108839 420171 657124 368491 675880 932234 576903 283596 038818 359375 / 91 > 5293 [i]
- extracting embedded OOA [i] would yield OOA(5293, 99, S5, 3, 272), 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 (21, 98)-sequence in base 5 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (21, m, 98)-net in base 5 with m > ∞ | [i] | ||
| 3 | No digital (21, 98)-sequence over F5 (for arbitrarily large k) | [i] | ||
| 4 | No digital (21, m, 98)-net over F5 with m > ∞ | [i] | ||