Information on Result #1856190
There is no (20, m, 28)-net in base 2 for arbitrarily large m, because m-reduction would yield (20, 133, 28)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2133, 28, S2, 5, 113), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 261336 857795 280739 939871 698507 597986 398208 / 19 > 2133 [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 (20, 27)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (20, 20+k, 28)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (20, m, 28)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (20, 20+k, 28)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (20, m, 28)-net over F2 with unbounded m | [i] | ||