Information on Result #1856214
There is no (5, m, 18)-net in base 3 for arbitrarily large m, because m-reduction would yield (5, 30, 18)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(330, 18, S3, 2, 25), but
- the linear programming bound for OOAs shows that M ≥ 105622 150764 554937 / 455 > 330 [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 (5, 17)-sequence in base 3 | [i] | Net from Sequence | |
| 2 | No (5, 5+k, 18)-net in base 3 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (5, m, 18)-net in base 3 with unbounded m | [i] | ||
| 4 | No digital (5, 5+k, 18)-net over F3 for arbitrarily large k | [i] | ||
| 5 | No digital (5, m, 18)-net over F3 with unbounded m | [i] | ||