Information on Result #1850235
There is no (40, m, 92)-net in base 3 for arbitrarily large m, because m-reduction would yield (40, 363, 92)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3363, 92, S3, 4, 323), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 168286 662303 730863 643615 296801 545555 681715 967451 921423 155000 514749 907683 286978 494846 457366 460224 244406 583604 225224 434212 599631 542753 099233 585309 765906 718871 299729 525745 776829 > 3363 [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 (40, 91)-sequence in base 3 | [i] | Net from Sequence | |
| 2 | No (40, 40+k, 92)-net in base 3 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (40, m, 92)-net in base 3 with unbounded m | [i] | ||
| 4 | No digital (40, 40+k, 92)-net over F3 for arbitrarily large k | [i] | ||
| 5 | No digital (40, m, 92)-net over F3 with unbounded m | [i] | ||