Information on Result #1857119
There is no (7, 39)-sequence in base 5, because net from sequence would yield (7, m, 40)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (7, 77, 40)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(577, 40, S5, 2, 70), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 49 630836 753181 660492 284521 524197 771213 948726 654052 734375 / 71 > 577 [i]
- extracting embedded OOA [i] would yield OOA(577, 40, S5, 2, 70), 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 (7, 39)-sequence in base 5 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (7, m, 39)-net in base 5 with m > ∞ | [i] | ||
| 3 | No digital (7, 39)-sequence over F5 (for arbitrarily large k) | [i] | ||
| 4 | No digital (7, m, 39)-net over F5 with m > ∞ | [i] | ||