IN SEARCH OF SPORADIC (280, 63,14) DIFFERENCE SETS

Abstract

In the book titled ”Symmetric design: an algebraic approach”, Eric Lander gave a wonderful exposition of difference sets and listed some abelian (v, k, λ) difference set parameters that were open for small values of k. One of such parameter sets is (280, 63, 14). Lander[1] and Kopilovich [2] showed that there are no (280, 63, 14) difference sets in the three abelian groups of order 280. Using restrictions imposed by the underlying subgroups of group of order 280, representation
theory and factorization of cyclotomic rings, we conclude that these difference sets may only exist in five of the thirty-seven non-abelian groups of order 280.