Information on Result #1856194
There is no (24, m, 32)-net in base 2 for arbitrarily large m, because m-reduction would yield (24, 185, 32)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2185, 32, S2, 6, 161), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1569 275433 846670 190958 947355 801916 604025 588861 116008 628224 / 27 > 2185 [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 (24, 31)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (24, 24+k, 32)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (24, m, 32)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (24, 24+k, 32)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (24, m, 32)-net over F2 with unbounded m | [i] | ||