Information on Result #1850238
There is no (41, m, 94)-net in base 3 for arbitrarily large m, because m-reduction would yield (41, 371, 94)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3371, 94, S3, 4, 330), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 354653 782470 898582 729208 760309 092060 019323 578542 789858 618462 492562 367387 864732 444902 243350 628745 646801 486471 706952 149392 189258 292134 783728 500628 270340 405073 223308 595605 657211 543715 / 331 > 3371 [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 (41, 93)-sequence in base 3 | [i] | Net from Sequence | |
| 2 | No (41, 41+k, 94)-net in base 3 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (41, m, 94)-net in base 3 with unbounded m | [i] | ||
| 4 | No digital (41, 41+k, 94)-net over F3 for arbitrarily large k | [i] | ||
| 5 | No digital (41, m, 94)-net over F3 with unbounded m | [i] | ||