Information on Result #1857123
There is no (11, 57)-sequence in base 5, because net from sequence would yield (11, m, 58)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (11, 113, 58)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5113, 58, S5, 2, 102), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1107 409718 022660 615507 187316 986333 208159 408447 723848 212262 964807 450771 331787 109375 / 103 > 5113 [i]
- extracting embedded OOA [i] would yield OOA(5113, 58, S5, 2, 102), 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 (11, 57)-sequence in base 5 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (11, m, 57)-net in base 5 with m > ∞ | [i] | ||
| 3 | No digital (11, 57)-sequence over F5 (for arbitrarily large k) | [i] | ||
| 4 | No digital (11, m, 57)-net over F5 with m > ∞ | [i] | ||