Information on Result #1856317
There is no (2, m, 49)-net in base 16 for arbitrarily large m, because m-reduction would yield (2, 45, 49)-net in base 16, but
- extracting embedded orthogonal array [i] would yield OA(1645, 49, S16, 43), but
- the linear programming bound shows that M ≥ 79 689768 125026 220634 634045 411816 077548 174434 353547 313152 / 47 > 1645 [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 (2, 48)-sequence in base 16 | [i] | Net from Sequence | |
| 2 | No (2, 2+k, 49)-net in base 16 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (2, m, 49)-net in base 16 with unbounded m | [i] | ||
| 4 | No digital (2, 2+k, 49)-net over F16 for arbitrarily large k | [i] | ||
| 5 | No digital (2, m, 49)-net over F16 with unbounded m | [i] | ||