Information on Result #1858724
There is no digital (4, m, 37)-net over F7 for arbitrarily large m, because m-reduction would yield digital (4, 32, 37)-net over F7, but
- extracting embedded orthogonal array [i] would yield linear OA(732, 37, F7, 28) (dual of [37, 5, 29]-code), but
- construction Y1 [i] would yield
- OA(731, 33, S7, 28), but
- the (dual) Plotkin bound shows that M ≥ 5522 138371 219603 231526 496005 / 29 > 731 [i]
- OA(75, 37, S7, 4), but
- discarding factors would yield OA(75, 31, S7, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 16927 > 75 [i]
- discarding factors would yield OA(75, 31, S7, 4), but
- OA(731, 33, S7, 28), 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 (4, 36)-sequence over F7 | [i] | Net from Sequence | |
| 2 | No digital (4, 4+k, 37)-net over F7 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No digital (4, m, 37)-net over F7 with unbounded m | [i] | ||