Primitive symmetric designs with prime power number of points

In this paper we either prove the non‐existence or give explicit construction of primitive symmetric (v, k, λ) designs with v=p^m<2500, p prime and m>1. The method of design construction is based on an automorphism group action; non‐existence results additionally include the theory of difference sets, multiplier theorems in particular. The research involves programming and wide‐range computations. We make use of software package GAP and the library of primitive groups which it contains. © 2009 Wiley Periodicals, Inc. J Combin Designs 18: 141–154, 2010