Information on Result #1856396
There is no (57, 66)-sequence in base 2, because net from sequence would yield (57, m, 67)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (57, 393, 67)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2393, 67, S2, 6, 336), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 9 844827 660206 338998 063191 843261 482770 882003 335161 414642 666888 796811 219058 939207 054525 522909 380525 482349 380843 146099 818496 / 337 > 2393 [i]
- extracting embedded OOA [i] would yield OOA(2393, 67, S2, 6, 336), 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 (57, 66)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (57, m, 66)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (57, 66)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (57, m, 66)-net over F2 with m > ∞ | [i] | ||