Information on Result #1856351
There is no (12, 18)-sequence in base 2, because net from sequence would yield (12, m, 19)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (12, 89, 19)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(289, 19, S2, 5, 77), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 9284 550294 640352 061743 431680 / 13 > 289 [i]
- extracting embedded OOA [i] would yield OOA(289, 19, S2, 5, 77), 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 (12, 18)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (12, m, 18)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (12, 18)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (12, m, 18)-net over F2 with m > ∞ | [i] | ||