Information on Result #1850217
There is no (34, m, 80)-net in base 3 for arbitrarily large m, because m-reduction would yield (34, 314, 80)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3314, 80, S3, 4, 280), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 241 601901 558808 255480 810106 750959 761525 496530 550725 667504 364320 172551 252618 533199 343528 859969 183401 331740 222554 999779 831546 868843 129811 039523 483186 441561 / 281 > 3314 [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 (34, 79)-sequence in base 3 | [i] | Net from Sequence | |
| 2 | No (34, 34+k, 80)-net in base 3 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (34, m, 80)-net in base 3 with unbounded m | [i] | ||
| 4 | No digital (34, 34+k, 80)-net over F3 for arbitrarily large k | [i] | ||
| 5 | No digital (34, m, 80)-net over F3 with unbounded m | [i] | ||