Speaker: Anamari Nakić

Title: Kramer-Mesner with Tactical Decomposition

Abstract: A \(t\)-\((v,k,\lambda)\) design is a finite incidence structure consisting of \(v\) points and a number of blocks (sets of points), such that each block contains exactly \(k\) points and every set of \(t\) distinct points is contained in exactly \(\lambda\) blocks. Although there are many known examples of \(t\)-designs, for many parameters the question of existence remains open. In order to construct new \(t\)-designs, it is practically impossible to complete an exhaustive search because the problem is of exponential complexity. It is necessary to add constraints to the search. We shall present a new approach in construction of \(t\)-designs admitting an action of an automorphism group. It is a combination of the well known Kramer-Mesner method and tactical decomposition and indexing. This new combination of two approaches can in many cases dramatically reduce the size of the Kramer-Mesner matrix and therefore \(t\)-designs can be constructed faster and more easily. We shall present an outline of this new technique as well as some new results for \(t\)-designs.