Information on Result #1856413
There is no (74, 83)-sequence in base 2, because net from sequence would yield (74, m, 84)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (74, 496, 84)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2496, 84, S2, 6, 422), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 9 820171 823688 425610 039569 090482 797456 649926 138129 194368 449874 104288 401389 214023 664649 810276 977712 471452 660052 382680 213027 651769 637656 179159 985582 768128 / 47 > 2496 [i]
- extracting embedded OOA [i] would yield OOA(2496, 84, S2, 6, 422), but
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 (74, 83)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (74, m, 83)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (74, 83)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (74, m, 83)-net over F2 with m > ∞ | [i] | ||