Information on Result #1873589
There is no digital (18, m, 45)-net over F3 with m > ∞, because logical equivalence would yield (18, 45)-sequence in base 3, but
- net from sequence [i] would yield (18, m, 46)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (18, 179, 46)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3179, 46, S3, 4, 161), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 27 273371 522594 140467 153112 393800 633219 287891 860116 798827 111671 686466 135591 950100 031709 > 3179 [i]
- extracting embedded OOA [i] would yield OOA(3179, 46, S3, 4, 161), but
- m-reduction [i] would yield (18, 179, 46)-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.