Information on Result #1856245
There is no (9, m, 38)-net in base 4 for arbitrarily large m, because m-reduction would yield (9, 110, 38)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4110, 38, S4, 3, 101), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 33 699933 333938 299743 333768 858774 538342 046430 528175 715601 379512 811520 / 17 > 4110 [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 (9, 37)-sequence in base 4 | [i] | Net from Sequence | |
| 2 | No (9, 9+k, 38)-net in base 4 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (9, m, 38)-net in base 4 with unbounded m | [i] | ||
| 4 | No digital (9, 9+k, 38)-net over F4 for arbitrarily large k | [i] | ||
| 5 | No digital (9, m, 38)-net over F4 with unbounded m | [i] | ||