Information on Result #1856225
There is no (16, m, 42)-net in base 3 for arbitrarily large m, because m-reduction would yield (16, 163, 42)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3163, 42, S3, 4, 147), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 26 544651 814199 643338 440247 651133 135698 218965 877468 993535 187581 097625 462811 569215 / 37 > 3163 [i]
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 (16, 41)-sequence in base 3 | [i] | Net from Sequence | |
| 2 | No (16, 16+k, 42)-net in base 3 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (16, m, 42)-net in base 3 with unbounded m | [i] | ||
| 4 | No digital (16, 16+k, 42)-net over F3 for arbitrarily large k | [i] | ||
| 5 | No digital (16, m, 42)-net over F3 with unbounded m | [i] | ||