Information on Result #1858733
There is no digital (3, m, 37)-net over F9 for arbitrarily large m, because m-reduction would yield digital (3, 30, 37)-net over F9, but
- extracting embedded orthogonal array [i] would yield linear OA(930, 37, F9, 27) (dual of [37, 7, 28]-code), but
- construction Y1 [i] would yield
- OA(929, 31, S9, 27), but
- the (dual) Plotkin bound shows that M ≥ 42391 158275 216203 514294 433201 / 7 > 929 [i]
- OA(97, 37, S9, 6), but
- the linear programming bound shows that M ≥ 8306 954271 / 1613 > 97 [i]
- OA(929, 31, S9, 27), but
- construction Y1 [i] would yield
Mode: Bound (linear).
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 digital (3, 36)-sequence over F9 | [i] | Net from Sequence | |
| 2 | No digital (3, 3+k, 37)-net over F9 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No digital (3, m, 37)-net over F9 with unbounded m | [i] | ||