Information on Result #1856174
There is no (4, m, 10)-net in base 2 for arbitrarily large m, because m-reduction would yield (4, 16, 10)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(216, 10, S2, 3, 12), but
- the linear programming bound for OOAs shows that M ≥ 83807 961088 / 1 262099 > 216 [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 (4, 9)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (4, 4+k, 10)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (4, m, 10)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (4, 4+k, 10)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (4, m, 10)-net over F2 with unbounded m | [i] | ||