Point sets with many unit circles (Q1099414)

Let f(n) denote the largest integer for which there are n points in the Euclidean plane with the property that there are f(n) distinct circles with the same radii passing through at least 3 of the n points. The authors establish \(f(3)=1\), \(f(4)=f(5)=4\), \(f(6)=8\), \(f(7)=12\), and announce that \(f(8)=16\).