Arbitrarily large planar integer-distance sets in general position

Determine whether, for every positive integer n, there exists an n-point set in the Euclidean plane such that all pairwise Euclidean distances are integers and the set contains no three collinear points and no four concyclic points.

Background

Within the discussion of examples for convex distance functions, the paper recalls classical constructions of large rational-distance point sets on a circle and notes that arbitrarily large finite non-collinear integer-distance sets can be obtained by scaling certain rational-distance configurations. However, these constructions typically violate stronger general-position constraints such as avoiding three collinear points or four concyclic points.

The cited open problem asks whether one can simultaneously achieve arbitrarily large size, integer pairwise distances, and general position (no three collinear and no four on a circle) in the Euclidean plane. The paper notes that the best current constructions under these constraints have only seven points, highlighting the gap between known examples and the desired arbitrarily large families.