An Algorithm for Finding Smallest Defining Sets of $t$-Designs

Abstract

A set of blocks which is a subset of a unique $t$-$(v,k,{\lambda }_t)$ design is called a $definingset$ 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.