On \((351, 126, 45)\)-Difference Sets

In this paper, it is proved that an abelian \((351, 126, 45)\)-difference set only exists in the groups with exponent \(39\). This fills two missing entries in Lopez and Sanchez’s table with answer “no”. Furthermore, if a Spence difference set \(D\) has Character Divisibility Property, then \(D\) is one of the difference sets constructed by Spence.