New infinite families of 3-designs from algebraic curves of higher genus over finite fields (Q1010599)

Summary: We give a simple method for computing the stabilizer subgroup of \[ D(f)=\{\alpha \in {\mathbb F}_q \mid \text{ there is a }\beta \in {\mathbb F}_q^{\times}\text{ such that }\beta^n=f(\alpha)\} \] in \(PSL_2({\mathbb F}_q)\), where \(q\) is a large odd prime power, \(n\) is a positive integer dividing \(q-1\) greater than 1, and \(f(x) \in {\mathbb F}_q[x]\). As an application, we construct new infinite families of 3-designs.