Information on Result #1856262
There is no (1, m, 12)-net in base 5 for arbitrarily large m, because m-reduction would yield (1, 11, 12)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(511, 12, S5, 2, 10), but
- the linear programming bound for OOAs shows that M ≥ 6103 515625 / 121 > 511 [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 (1, 11)-sequence in base 5 | [i] | Net from Sequence | |
| 2 | No (1, 1+k, 12)-net in base 5 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (1, m, 12)-net in base 5 with unbounded m | [i] | ||
| 4 | No digital (1, 1+k, 12)-net over F5 for arbitrarily large k | [i] | ||
| 5 | No digital (1, m, 12)-net over F5 with unbounded m | [i] | ||