  Geometrical objects with integral sides have attracted mathematicians for
ages. For example, the problem to prove or to disprove the existence of a
perfect box, that is, a rectangular parallelepiped with all edges, face
diagonals and space diagonals of integer lengths, remains open. More generally
an integral point set $\mathcal{P}$ is a set of $n$ points in the
$m$-dimensional Euclidean space $\mathbb{E}^m$ with pairwise integral distances
where the largest occurring distance is called its diameter. From the
combinatorial point of view there is a natural interest in the determination of
the smallest possible diameter $d(m,n)$ for given parameters $m$ and $n$. We
give some new upper bounds for the minimum diameter $d(m,n)$ and some exact
values.
