Information on Result #1856238
There is no (2, m, 13)-net in base 4 for arbitrarily large m, because m-reduction would yield (2, 16, 13)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(416, 13, S4, 3, 14), but
- the linear programming bound for OOAs shows that M ≥ 176093 659136 / 37 > 416 [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 (2, 12)-sequence in base 4 | [i] | Net from Sequence | |
| 2 | No (2, 2+k, 13)-net in base 4 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (2, m, 13)-net in base 4 with unbounded m | [i] | ||
| 4 | No digital (2, 2+k, 13)-net over F4 for arbitrarily large k | [i] | ||
| 5 | No digital (2, m, 13)-net over F4 with unbounded m | [i] | ||