Information on Result #1856216
There is no (7, m, 23)-net in base 3 for arbitrarily large m, because m-reduction would yield (7, 35, 23)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(335, 23, S3, 2, 28), but
- the linear programming bound for OOAs shows that M ≥ 1 050995 602043 303294 963563 814764 130877 / 19 578586 921145 663665 > 335 [i]
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 (7, 22)-sequence in base 3 | [i] | Net from Sequence | |
| 2 | No (7, 7+k, 23)-net in base 3 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (7, m, 23)-net in base 3 with unbounded m | [i] | ||
| 4 | No digital (7, 7+k, 23)-net over F3 for arbitrarily large k | [i] | ||
| 5 | No digital (7, m, 23)-net over F3 with unbounded m | [i] | ||