Information on Result #1873619
There is no digital (33, m, 77)-net over F3 with m > ∞, because logical equivalence would yield (33, 77)-sequence in base 3, but
- net from sequence [i] would yield (33, m, 78)-net in base 3 for arbitrarily large m, but
- m-reduction [i] 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]
- extracting embedded OOA [i] would yield OOA(3306, 78, S3, 4, 273), but
- m-reduction [i] would yield (33, 306, 78)-net in base 3, but
Mode: Bound (linear).
Optimality
Show details for fixed t and s.
Other Results with Identical Parameters
None.
Depending Results
None.