Point sets that minimize (≤k)-edges, 3-decomposable drawings, and the rectilinear crossing number of K30

There are two properties shared by all known crossing-minimizing geometric drawings of K"n, for n a multiple of 3. First, the underlying n-point set of these drawings minimizes the number of (@?k)-edges, that means, has exactly 3(k+22)(@?k)-edges, for all 0@?k