Information on Result #1850220
There is no (35, m, 82)-net in base 3 for arbitrarily large m, because m-reduction would yield (35, 322, 82)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3322, 82, S3, 4, 287), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 21478 998321 508685 151891 532661 152398 311230 118386 765733 123253 852366 559739 409623 256380 662504 746040 817020 833978 322267 663353 316788 705688 003932 660075 517428 768045 / 4 > 3322 [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 (35, 81)-sequence in base 3 | [i] | Net from Sequence | |
| 2 | No (35, 35+k, 82)-net in base 3 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (35, m, 82)-net in base 3 with unbounded m | [i] | ||
| 4 | No digital (35, 35+k, 82)-net over F3 for arbitrarily large k | [i] | ||
| 5 | No digital (35, m, 82)-net over F3 with unbounded m | [i] | ||