Information on Result #1856172
There is no (2, m, 7)-net in base 2 for arbitrarily large m, because m-reduction would yield (2, 10, 7)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(210, 7, S2, 3, 8), but
- the linear programming bound for OOAs shows that M ≥ 1 314304 / 1193 > 210 [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, 6)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (2, 2+k, 7)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (2, m, 7)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (2, 2+k, 7)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (2, m, 7)-net over F2 with unbounded m | [i] | ||