Given a (finite) perfect difference set, it is easy to create a finite projective plane. I'm wondering:
Given a finite projective plane, does there necessarily exist a corresponding perfect difference set? What if we restrict ourselves to planes of prime power order, or Desarguesian planes?
If such a perfect difference set exists for a given finite projective plane, is there some procedure/algorithm to derive that set from the plane? What if we consider the restrictions in the previous question?
Given two perfect difference sets of the same size, must they both correspond to the same projective plane? Are there counterexamples?