Information on Result #1856388
There is no (49, 57)-sequence in base 2, because net from sequence would yield (49, m, 58)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (49, 398, 58)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2398, 58, S2, 7, 349), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 127 821368 965301 975187 967999 014149 087779 320436 745046 563885 117638 148762 057289 833639 134167 444987 366822 656077 207012 651000 922112 / 175 > 2398 [i]
- extracting embedded OOA [i] would yield OOA(2398, 58, S2, 7, 349), 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 (49, 57)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (49, m, 57)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (49, 57)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (49, m, 57)-net over F2 with m > ∞ | [i] | ||