Erdős–Noll conjecture on the number of non-isomorphic clusters

An $n_m$-cluster is an integral point set in general position consisting of $n$ points in the integer grid $\mathbb{Z}^m$. Erdős–Noll conjecture. For any $m>1$ and $n>1$, there exists either no $n_m$-cluster or an infinite number of non-isomorphic $n_m$-clusters. The conjecture concerns whether such clusters, once they exist, necessarily occur in infinitely many non-isomorphic forms; the source provides no evidence of a resolution.