Information on Result #1856249
There is no (13, m, 51)-net in base 4 for arbitrarily large m, because m-reduction would yield (13, 149, 51)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4149, 51, S4, 3, 136), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 95 740690 887720 846054 616947 355240 773569 419014 502299 003779 898601 119655 921088 876825 190619 676672 / 137 > 4149 [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 (13, 50)-sequence in base 4 | [i] | Net from Sequence | |
| 2 | No (13, 13+k, 51)-net in base 4 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (13, m, 51)-net in base 4 with unbounded m | [i] | ||
| 4 | No digital (13, 13+k, 51)-net over F4 for arbitrarily large k | [i] | ||
| 5 | No digital (13, m, 51)-net over F4 with unbounded m | [i] | ||