An Algorithm for Finding Smallest Defining Sets of \(t\)-Designs

A set of blocks which is a subset of a unique \(t\)-\((v,k,\lambda_t)\) design is called a \({defining \; set}\) of that design. Using known results, an algorithm for finding smallest defining sets of any \(t\)-\((v,k,\lambda_t)\) design is described. Then the results of this algorithm as applied to the two \(2\)-\((13,3,1)\) designs are given.