automorphism group of a possible 2-(121, 16, 2) symmetric design

let d be a symmetric 2-(121, 16, 2) design with the automorphism group of aut(d). in this paper the order of automorphism of prime order of aut(d) is studied, and some results are obtained about the number of fixed points of these automorphisms. also we will show that |aut(d)|=2p 3q 5r 7s 11t 13u, where p, q, r, s, t and u are non-negative integers such that r, s, t, u ? 1. in addition we present some general results on the automorphisms with prime order of a symmetric design and some general results on the automorphism groups of a symmetric design are given and in section 3, we prove a series of lemma. based on them we can prove main theorem. one of the reasons for the emergence and growth of block designs is the combined irrigation of fields having a lot of patches, at the end of the paper, there is offered an application of block design in modern irrigation.