Equations for coefficients of tactical decomposition matrices for $$t$$ -designs

Abstract

Equations for coefficients of tactical decomposition matrices for 2-designs are well-known and they have been used for constructions of many examples of 2-designs. In this paper, we generalize these equations and propose an explicit equation system for coefficients of tactical decomposition matrices for $$t\text{-}(v,k,\lambda _t)$$ designs, for any integer value of $$t.$$