Existence of (v, k, 2) difference sets with k < 2030 and √ k − 2 is a natural number

Abstract

(v, k, 2) symmetric designs(or Biplanes) are known to exist for some integer values k < 16. This paper investigates the existence of a class of (v, k, 2) dierence sets with 2 ≤ √k − 2 ≤ 45 and √k − 2 is an integer using variance technique, representation, group and algebraic number Theories. Our results indicate that most of these parameters do not exist.