I want to find an example of a basis of a lattice of dimension $n$ such that LLL algorithm can't find the shortest vector of the lattice, and such that the shortest vector of this lattice, say $b=c_1b_1+\cdots+c_nb_n$, has small $c_i$, i.e., $c_i \in \{-r,\ldots,r\}$ with small $r$.
Note that $b_i \in \mathbb{Z}^n$ and $c_i \in \mathbb{Z}$.
Such example must satisfy $\log_2(2(r+1)) \cdot n \leq 15$, say $n=5$ and $r=4$.
The idea here is to have a treatable value for $2^{\log_2(2(r+1)) \cdot n}$.
I can't find any lattice satisfying this.
Thanks in advance.