Information on Result #1858725
There is no digital (1, m, 15)-net over F8 for arbitrarily large m, because m-reduction would yield digital (1, 9, 15)-net over F8, but
- extracting embedded orthogonal array [i] would yield linear OA(89, 15, F8, 8) (dual of [15, 6, 9]-code), but
- “MPa†bound on codes from Brouwer’s database [i]
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 (1, 14)-sequence over F8 | [i] | Net from Sequence | |
| 2 | No digital (1, 1+k, 15)-net over F8 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No digital (1, m, 15)-net over F8 with unbounded m | [i] | ||