Information on Result #1858729
There is no digital (6, m, 58)-net over F8 for arbitrarily large m, because m-reduction would yield digital (6, 48, 58)-net over F8, but
- extracting embedded orthogonal array [i] would yield linear OA(848, 58, F8, 42) (dual of [58, 10, 43]-code), but
- construction Y1 [i] would yield
- linear OA(847, 50, F8, 42) (dual of [50, 3, 43]-code), but
- “Hi4†bound on codes from Brouwer’s database [i]
- OA(810, 58, S8, 8), but
- discarding factors would yield OA(810, 57, S8, 8), but
- the linear programming bound shows that M ≥ 1426 626655 027200 / 1 315507 > 810 [i]
- discarding factors would yield OA(810, 57, S8, 8), but
- linear OA(847, 50, F8, 42) (dual of [50, 3, 43]-code), 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 (6, 57)-sequence over F8 | [i] | Net from Sequence | |
| 2 | No digital (6, 6+k, 58)-net over F8 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No digital (6, m, 58)-net over F8 with unbounded m | [i] | ||