Some Designs from the Conjugacy Classes of Linear Groups

In this paper, we apply a recently introduced method for constructing 1-designs to determine several 1-designs invariant under the PSL 2 (q) . These designs are obtained from the subgroups and conjugacy classes of elements in the group PSL 2 (q), where q is a power of an odd prime. The proposed method enables the construction of 1-designs from any subgroup of PSL 2 (q), resulting in a variety of new designs, most of which are distinct from those previously known.