Information on Result #1856358
There is no (19, 26)-sequence in base 2, because net from sequence would yield (19, m, 27)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (19, 128, 27)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2128, 27, S2, 5, 109), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 25180 895152 149446 296289 720949 950847 647744 / 55 > 2128 [i]
- extracting embedded OOA [i] would yield OOA(2128, 27, S2, 5, 109), 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 (19, 26)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (19, m, 26)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (19, 26)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (19, m, 26)-net over F2 with m > ∞ | [i] | ||