Information on Result #1850196
There is no (27, m, 65)-net in base 3 for arbitrarily large m, because m-reduction would yield (27, 255, 65)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3255, 65, S3, 4, 228), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 12371 752261 565881 216079 641024 279855 977165 477721 959093 281252 829374 273210 464049 212798 749157 454715 755247 441238 233108 852049 761369 / 229 > 3255 [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 (27, 64)-sequence in base 3 | [i] | Net from Sequence | |
| 2 | No (27, 27+k, 65)-net in base 3 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (27, m, 65)-net in base 3 with unbounded m | [i] | ||
| 4 | No digital (27, 27+k, 65)-net over F3 for arbitrarily large k | [i] | ||
| 5 | No digital (27, m, 65)-net over F3 with unbounded m | [i] | ||