Information on Result #1856318
There is no (3, m, 65)-net in base 16 for arbitrarily large m, because m-reduction would yield (3, 61, 65)-net in base 16, but
- extracting embedded orthogonal array [i] would yield OA(1661, 65, S16, 58), but
- the linear programming bound shows that M ≥ 159214 122701 309768 707410 104386 945873 298246 228915 255775 554254 178010 880553 254912 / 5487 > 1661 [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 (3, 64)-sequence in base 16 | [i] | Net from Sequence | |
| 2 | No (3, 3+k, 65)-net in base 16 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (3, m, 65)-net in base 16 with unbounded m | [i] | ||
| 4 | No digital (3, 3+k, 65)-net over F16 for arbitrarily large k | [i] | ||
| 5 | No digital (3, m, 65)-net over F16 with unbounded m | [i] | ||