Information on Result #1856861
There is no (10, 40)-sequence in base 4, because net from sequence would yield (10, m, 41)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (10, 119, 41)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4119, 41, S4, 3, 109), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 25 619282 439286 572778 957813 760772 318479 498516 504696 474892 763289 918742 986752 / 55 > 4119 [i]
- extracting embedded OOA [i] would yield OOA(4119, 41, S4, 3, 109), 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 (10, 40)-sequence in base 4 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (10, m, 40)-net in base 4 with m > ∞ | [i] | ||
| 3 | No digital (10, 40)-sequence over F4 (for arbitrarily large k) | [i] | ||
| 4 | No digital (10, m, 40)-net over F4 with m > ∞ | [i] | ||