Information on Result #1856421
There is no (82, 91)-sequence in base 2, because net from sequence would yield (82, m, 92)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (82, 635, 92)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2635, 92, S2, 7, 553), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 46 765016 330627 500991 072008 958427 986080 155592 199297 739288 436723 308467 570463 888943 211685 606316 003056 847731 083673 129342 674934 559223 394098 239482 089778 527152 695429 582945 412192 715738 349460 470527 688704 / 277 > 2635 [i]
- extracting embedded OOA [i] would yield OOA(2635, 92, S2, 7, 553), 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 (82, 91)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (82, m, 91)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (82, 91)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (82, m, 91)-net over F2 with m > ∞ | [i] | ||