Information on Result #1856393
There is no (54, 62)-sequence in base 2, because net from sequence would yield (54, m, 63)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (54, 433, 63)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2433, 63, S2, 7, 379), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2 140501 003861 269071 594535 750158 460619 052929 422190 130396 031610 236234 487649 625942 980986 860241 512395 754291 186014 862203 557451 968049 840128 / 95 > 2433 [i]
- extracting embedded OOA [i] would yield OOA(2433, 63, S2, 7, 379), 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 (54, 62)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (54, m, 62)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (54, 62)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (54, m, 62)-net over F2 with m > ∞ | [i] | ||