Information on Result #1849533
There is no (40, m, 49)-net in base 2 for arbitrarily large m, because m-reduction would yield (40, 286, 49)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2286, 49, S2, 6, 246), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 39288 535676 373144 730275 197603 598846 367936 035912 990469 677796 654174 559600 263990 136667 111424 / 247 > 2286 [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 (40, 48)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (40, 40+k, 49)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (40, m, 49)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (40, 40+k, 49)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (40, m, 49)-net over F2 with unbounded m | [i] | ||