Information on Result #1856366
There is no (27, 34)-sequence in base 2, because net from sequence would yield (27, m, 35)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (27, 203, 35)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2203, 35, S2, 6, 176), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 797 041269 952459 176668 813197 801216 650851 012684 916265 246309 482496 / 59 > 2203 [i]
- extracting embedded OOA [i] would yield OOA(2203, 35, S2, 6, 176), 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 (27, 34)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (27, m, 34)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (27, 34)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (27, m, 34)-net over F2 with m > ∞ | [i] | ||