Information on Result #1858344
There is no (1, 100)-sequence in base 49, because net from sequence would yield (1, m, 101)-net in base 49 for arbitrarily large m, but
- m-reduction [i] would yield (1, 99, 101)-net in base 49, but
- extracting embedded OOA [i] would yield OA(4999, 101, S49, 98), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 10 461838 291314 357175 018899 611816 813659 819188 550170 233659 950140 084035 125767 424262 251774 382614 909364 050293 065248 252546 314174 063180 343683 591188 150754 267339 816534 637456 120001 / 33 > 4999 [i]
- extracting embedded OOA [i] would yield OA(4999, 101, S49, 98), 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 (1, 100)-sequence in base 49 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (1, m, 100)-net in base 49 with m > ∞ | [i] | ||
| 3 | No digital (1, 100)-sequence over F49 (for arbitrarily large k) | [i] | ||
| 4 | No digital (1, m, 100)-net over F49 with m > ∞ | [i] | ||