Concerning Difference Sets

Abstract

A set of integers {a₀, a₁, … , a_n} is said to be a difference set modulo N if the set of differences {a_i — a_j (i,j = 0, 1, … , n) contains each non-zero residue mod N exactly once. It follows that N and n are connected by the relation N = n² + n + 1. If {a₀, a₁ … a_n} is a difference set mod N, so is the set {a₀ + s, a₁ + s, … , a_n + s} (s = 0, 1, … , N). These difference sets form a finite projective plane of N points, with each difference set constituting a line in the plane.