Information on Result #1856206
There is no (36, m, 45)-net in base 2 for arbitrarily large m, because m-reduction would yield (36, 218, 45)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2218, 45, S2, 5, 182), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 28 644943 333847 554781 833703 529958 357590 739465 948949 358261 172585 889792 / 61 > 2218 [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 (36, 44)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (36, 36+k, 45)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (36, m, 45)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (36, 36+k, 45)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (36, m, 45)-net over F2 with unbounded m | [i] | ||