Information on Result #1856200
There is no (30, m, 39)-net in base 2 for arbitrarily large m, because m-reduction would yield (30, 187, 39)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2187, 39, S2, 5, 157), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 19615 942923 083377 386986 841947 523957 550319 860763 950107 852800 / 79 > 2187 [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 (30, 38)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (30, 30+k, 39)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (30, m, 39)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (30, 30+k, 39)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (30, m, 39)-net over F2 with unbounded m | [i] | ||