Information on Result #1858744
There is no digital (3, m, 132)-net over F32 for arbitrarily large m, because m-reduction would yield digital (3, 99, 132)-net over F32, but
- extracting embedded orthogonal array [i] would yield linear OA(3299, 132, F32, 96) (dual of [132, 33, 97]-code), but
- residual code [i] would yield OA(323, 35, S32, 3), but
- 1 times truncation [i] would yield OA(322, 34, S32, 2), but
- bound for OAs with strength k = 2 [i]
- the Rao or (dual) Hamming bound shows that M ≥ 1055 > 322 [i]
- 1 times truncation [i] would yield OA(322, 34, S32, 2), but
- residual code [i] would yield OA(323, 35, S32, 3), but
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, 131)-sequence over F32 | [i] | Net from Sequence | |
| 2 | No digital (3, 3+k, 132)-net over F32 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No digital (3, m, 132)-net over F32 with unbounded m | [i] | ||