Information on Result #1849569
There is no (52, m, 61)-net in base 2 for arbitrarily large m, because m-reduction would yield (52, 419, 61)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2419, 61, S2, 7, 367), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 32 999913 962009 210059 679612 176995 930308 233961 773576 918466 689667 860098 337098 516662 383593 445385 150587 019591 753304 289166 046548 459520 / 23 > 2419 [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 (52, 60)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (52, 52+k, 61)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (52, m, 61)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (52, 52+k, 61)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (52, m, 61)-net over F2 with unbounded m | [i] | ||