Information on Result #1856195
There is no (25, m, 33)-net in base 2 for arbitrarily large m, because m-reduction would yield (25, 191, 33)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2191, 33, S2, 6, 166), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 596324 664861 734672 564399 995204 728309 529723 767224 083278 725120 / 167 > 2191 [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 (25, 32)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (25, 25+k, 33)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (25, m, 33)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (25, 25+k, 33)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (25, m, 33)-net over F2 with unbounded m | [i] | ||