Information on Result #1856349
There is no (10, 16)-sequence in base 2, because net from sequence would yield (10, m, 17)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (10, 62, 17)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(262, 17, S2, 4, 52), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 276 701161 105643 274240 / 53 > 262 [i]
- extracting embedded OOA [i] would yield OOA(262, 17, S2, 4, 52), 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 (10, 16)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (10, m, 16)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (10, 16)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (10, m, 16)-net over F2 with m > ∞ | [i] | ||