Information on Result #1850211
There is no (32, m, 76)-net in base 3 for arbitrarily large m, because m-reduction would yield (32, 298, 76)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3298, 76, S3, 4, 266), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 962111 199839 766722 542339 725809 932528 852646 303963 169922 757882 724456 622292 877486 764511 136288 231541 493231 590276 981904 581280 327015 836308 306102 112681 / 89 > 3298 [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 (32, 75)-sequence in base 3 | [i] | Net from Sequence | |
| 2 | No (32, 32+k, 76)-net in base 3 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (32, m, 76)-net in base 3 with unbounded m | [i] | ||
| 4 | No digital (32, 32+k, 76)-net over F3 for arbitrarily large k | [i] | ||
| 5 | No digital (32, m, 76)-net over F3 with unbounded m | [i] | ||