Do (1276, 51, 2) difference sets exist?

Adegoke S. A. Osifodunrin

It is known that the $(v, k, 2)$ symmetric designs otherwise called biplanes exist for some integer values $k < 16$. Based on the relationship between symmetric designs and difference sets, we investigate the existence of (1276, 51, 2) difference sets. Some authors have established the non existence of abelian (1276, 51, 2) difference sets. Using representation and algebraic number theories, we show that this difference sets do not exist in most groups of order 1276.