Information on Result #1856227
There is no (18, m, 46)-net in base 3 for arbitrarily large m, because m-reduction 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]
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 (18, 45)-sequence in base 3 | [i] | Net from Sequence | |
| 2 | No (18, 18+k, 46)-net in base 3 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (18, m, 46)-net in base 3 with unbounded m | [i] | ||
| 4 | No digital (18, 18+k, 46)-net over F3 for arbitrarily large k | [i] | ||
| 5 | No digital (18, m, 46)-net over F3 with unbounded m | [i] | ||