Information on Result #1856202
There is no (32, m, 41)-net in base 2 for arbitrarily large m, because m-reduction would yield (32, 197, 41)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2197, 41, S2, 5, 165), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 18 479787 508978 388168 732564 061923 369929 005334 428502 117605 965824 / 83 > 2197 [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 (32, 40)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (32, 32+k, 41)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (32, m, 41)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (32, 32+k, 41)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (32, m, 41)-net over F2 with unbounded m | [i] | ||