Information on Result #1856631
There is no (31, 73)-sequence in base 3, because net from sequence would yield (31, m, 74)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (31, 290, 74)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3290, 74, S3, 4, 259), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 229 508652 590225 900915 193766 377529 564949 108466 983495 168600 256377 208056 541526 061551 978631 651838 527412 783227 454480 502657 288667 678716 723464 947451 / 65 > 3290 [i]
- extracting embedded OOA [i] would yield OOA(3290, 74, S3, 4, 259), 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 (31, 73)-sequence in base 3 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (31, m, 73)-net in base 3 with m > ∞ | [i] | ||
| 3 | No digital (31, 73)-sequence over F3 (for arbitrarily large k) | [i] | ||
| 4 | No digital (31, m, 73)-net over F3 with m > ∞ | [i] | ||