Information on Result #1856395
There is no (56, 65)-sequence in base 2, because net from sequence would yield (56, m, 66)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (56, 387, 66)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2387, 66, S2, 6, 331), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 39086 790146 823323 378580 807779 342464 894639 101356 301723 094604 707057 011755 997325 232926 522952 124845 836315 680174 966384 361472 / 83 > 2387 [i]
- extracting embedded OOA [i] would yield OOA(2387, 66, S2, 6, 331), 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 (56, 65)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (56, m, 65)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (56, 65)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (56, m, 65)-net over F2 with m > ∞ | [i] | ||