Information on Result #1850214
There is no (33, m, 78)-net in base 3 for arbitrarily large m, because m-reduction would yield (33, 306, 78)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3306, 78, S3, 4, 273), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 18861 044876 171365 032460 891378 731510 262175 334446 954617 334477 012069 187758 800113 000272 170386 204336 978033 414539 996710 032217 212888 597833 190329 515478 183781 / 137 > 3306 [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 (33, 77)-sequence in base 3 | [i] | Net from Sequence | |
| 2 | No (33, 33+k, 78)-net in base 3 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (33, m, 78)-net in base 3 with unbounded m | [i] | ||
| 4 | No digital (33, 33+k, 78)-net over F3 for arbitrarily large k | [i] | ||
| 5 | No digital (33, m, 78)-net over F3 with unbounded m | [i] | ||