Information on Result #1857134
There is no (22, 102)-sequence in base 5, because net from sequence would yield (22, m, 103)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (22, 305, 103)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5305, 103, S5, 3, 283), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 130397 795171 970861 566606 442554 322946 766529 162050 766629 073275 523425 282483 328545 577437 221350 044741 629982 362688 619698 815523 006022 838089 406595 855824 612515 394341 700473 113899 715082 476815 641854 273053 468205 034732 818603 515625 / 71 > 5305 [i]
- extracting embedded OOA [i] would yield OOA(5305, 103, S5, 3, 283), 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, 102)-sequence in base 5 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (22, m, 102)-net in base 5 with m > ∞ | [i] | ||
| 3 | No digital (22, 102)-sequence over F5 (for arbitrarily large k) | [i] | ||
| 4 | No digital (22, m, 102)-net over F5 with m > ∞ | [i] | ||