Information on Result #1856176
There is no (6, m, 12)-net in base 2 for arbitrarily large m, because m-reduction would yield (6, 43, 12)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(243, 12, S2, 4, 37), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 175 921860 444160 / 19 > 243 [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 (6, 11)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (6, 6+k, 12)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (6, m, 12)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (6, 6+k, 12)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (6, m, 12)-net over F2 with unbounded m | [i] | ||