Information on Result #1849608
There is no (65, m, 75)-net in base 2 for arbitrarily large m, because m-reduction would yield (65, 441, 75)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2441, 75, S2, 6, 376), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2407 653274 229197 824944 635113 629015 020046 437007 276741 074682 436284 785867 641875 630621 018007 855489 341810 920025 852820 756714 404833 367894 786048 / 377 > 2441 [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 (65, 74)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (65, 65+k, 75)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (65, m, 75)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (65, 65+k, 75)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (65, m, 75)-net over F2 with unbounded m | [i] | ||