Information on Result #1856226
There is no (17, m, 44)-net in base 3 for arbitrarily large m, because m-reduction would yield (17, 171, 44)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3171, 44, S3, 4, 154), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 685027 211508 324515 777792 095033 732379 709657 564813 491328 565171 830353 981268 593042 103819 / 155 > 3171 [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 (17, 43)-sequence in base 3 | [i] | Net from Sequence | |
| 2 | No (17, 17+k, 44)-net in base 3 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (17, m, 44)-net in base 3 with unbounded m | [i] | ||
| 4 | No digital (17, 17+k, 44)-net over F3 for arbitrarily large k | [i] | ||
| 5 | No digital (17, m, 44)-net over F3 with unbounded m | [i] | ||