Information on Result #1856218
There is no (9, m, 27)-net in base 3 for arbitrarily large m, because m-reduction would yield (9, 77, 27)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(377, 27, S3, 3, 68), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 147 808829 414345 923316 083210 206383 297601 / 23 > 377 [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 (9, 26)-sequence in base 3 | [i] | Net from Sequence | |
| 2 | No (9, 9+k, 27)-net in base 3 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (9, m, 27)-net in base 3 with unbounded m | [i] | ||
| 4 | No digital (9, 9+k, 27)-net over F3 for arbitrarily large k | [i] | ||
| 5 | No digital (9, m, 27)-net over F3 with unbounded m | [i] | ||