Information on Result #1856219
There is no (10, m, 29)-net in base 3 for arbitrarily large m, because m-reduction would yield (10, 83, 29)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(383, 29, S3, 3, 73), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 155642 697373 306257 251835 620347 321612 373853 / 37 > 383 [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 (10, 28)-sequence in base 3 | [i] | Net from Sequence | |
| 2 | No (10, 10+k, 29)-net in base 3 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (10, m, 29)-net in base 3 with unbounded m | [i] | ||
| 4 | No digital (10, 10+k, 29)-net over F3 for arbitrarily large k | [i] | ||
| 5 | No digital (10, m, 29)-net over F3 with unbounded m | [i] | ||