Information on Result #1856422
There is no (83, 92)-sequence in base 2, because net from sequence would yield (83, m, 93)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (83, 642, 93)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2642, 93, S2, 7, 559), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 743 677820 672417 820638 510971 729147 485957 596246 681515 268684 408380 417581 852255 014414 000463 788244 731538 163918 696460 495888 391642 258869 584196 393715 183795 114720 912685 075131 920723 186863 508493 336196 415488 / 35 > 2642 [i]
- extracting embedded OOA [i] would yield OOA(2642, 93, S2, 7, 559), 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 (83, 92)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (83, m, 92)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (83, 92)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (83, m, 92)-net over F2 with m > ∞ | [i] | ||