Simulations on the combinatorial structure of D-optimal designs

In this work we present the results of several simulations on main-effect factorial designs. The goal of such simulations is to investigate the connections between the $D$-optimality of a design and its geometrical structure. By means of a combinatorial object, namely the circuit basis of the design matrix, we show that it is possible to define a simple index that exhibits strong connections with the $D$-optimality.