Inclusion-maximal integral point sets over finite fields
Michael Kiermaier, Sascha Kurz · EPub Bayreuth (University of Bayreuth) · 2007
We consider integral point sets in affine planes over finite fields.Here an integral point set is a set of points in F 2 q where the formally defined Euclidean distance of every pair of points is an element of Fq.From another point of view we consider point sets over F 2 q with few and prescribed directions.So this is related to Rédei's work.Another motivation comes from the field of ordinary integral point sets in Euclidean spaces E m .In this article we study the spectrum of integral point sets over Fq which are maximal with respect to inclusion.We give some theoretical results, constructions, conjectures, and some numerical data.