Information on Result #1850202
There is no (29, m, 69)-net in base 3 for arbitrarily large m, because m-reduction would yield (29, 271, 69)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3271, 69, S3, 4, 242), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2142 368937 253103 043834 638591 707247 385061 383828 483530 475078 497325 497761 213758 635430 004735 714829 845784 822552 287049 510582 282468 757069 > 3271 [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 (29, 68)-sequence in base 3 | [i] | Net from Sequence | |
| 2 | No (29, 29+k, 69)-net in base 3 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (29, m, 69)-net in base 3 with unbounded m | [i] | ||
| 4 | No digital (29, 29+k, 69)-net over F3 for arbitrarily large k | [i] | ||
| 5 | No digital (29, m, 69)-net over F3 with unbounded m | [i] | ||