Simulations on the combinatorial structure of D-optimal designs

TL;DR

This paper investigates the relationship between D-optimality and the geometric structure of factorial designs using combinatorial circuit bases, proposing a simple index that correlates strongly with optimality.

Contribution

It introduces a novel combinatorial approach using circuit bases to analyze D-optimality in factorial designs, revealing new connections between geometry and optimality.

Findings

The circuit basis index correlates strongly with D-optimality.

Simulations demonstrate the effectiveness of the index in identifying optimal designs.

The approach provides a new perspective on the structure of optimal factorial designs.

Abstract

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.