Information on Result #1856229
There is no (20, m, 51)-net in base 3 for arbitrarily large m, because m-reduction would yield (20, 148, 51)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3148, 51, S3, 3, 128), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 849942 425175 634864 623503 912258 483220 932365 501948 614869 075922 026508 741245 / 43 > 3148 [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 (20, 50)-sequence in base 3 | [i] | Net from Sequence | |
| 2 | No (20, 20+k, 51)-net in base 3 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (20, m, 51)-net in base 3 with unbounded m | [i] | ||
| 4 | No digital (20, 20+k, 51)-net over F3 for arbitrarily large k | [i] | ||
| 5 | No digital (20, m, 51)-net over F3 with unbounded m | [i] | ||