Difference sets with few character values
The known families of difference sets can be subdivided into three classes: difference sets with Singer parameters, cyclotomic difference sets, and difference sets with gcd\((v,n)>1\). It is remarkable that all the known difference sets with gcd\((v,n)>1\) have the so-called character divisibility property. Jungnickel and Schmidt (Difference sets: an update. London Math. Soc. Lecture Note Ser., vol. 245, pp. 89112, Cambridge University Press, Cambridge 1997) posed the problem of constructing difference sets with gcd\((v,n)>1\) that do not satisfy this property. In an attempt to attack this problem, we use difference sets with three nontrivial character values as candidates, and get some necessary conditions.
difference sets character values character divisible property association schemes 05e30 05b10