Information on Result #1849605
There is no (64, m, 74)-net in base 2 for arbitrarily large m, because m-reduction would yield (64, 435, 74)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2435, 74, S2, 6, 371), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3 194115 487627 178718 234333 140132 832426 358775 510832 940694 596392 476868 043746 592080 717742 050515 831968 793968 194675 027536 914746 978229 813248 / 31 > 2435 [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 (64, 73)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (64, 64+k, 74)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (64, m, 74)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (64, 64+k, 74)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (64, m, 74)-net over F2 with unbounded m | [i] | ||