Smallest defining sets of some STS(19) (Q2747199)

A Steiner triple system \(D\) on \(v\) points, denoted \(\text{STS}(v),\) consists in a set \(V\) with cardinal \(v\) added with a collection \(B\) of 3-subsets of \(V\) such that each pair in \(V\) is included in exactly one element of \(B.\) A generalization of such a definition is given by \(t\)-\((v,k,\lambda)\) designs. A defining set of \(D\) is a collection of 3-subsets that defines uniquely \(D.\) This paper determines the size of smallest defining sets for the STS(19) which have automorphism group orders of at least 9. The method is algorithmic. The results required a great deal of computation, so that progress much beyond \(v=19\) for general STS will not be obtained using this techniques.