Optimal Regular Graph Designs

TL;DR

This paper investigates optimal regular graph designs in experimental design theory, demonstrating their optimality under certain criteria through an extensive computer search for systems with up to 20 points.

Contribution

It provides the first comprehensive computer search results identifying optimal regular graph designs for large systems within specified parameters.

Findings

Regular graph designs are often A- and D-optimal when the number of blocks is large enough.

The paper identifies the best regular graph designs for systems with up to 20 points and specific parameter constraints.

Optimal designs are characterized for systems where r(k-1)-(v-1)[r(k-1)/(v-1)]<=9.

Abstract

A typical problem in optimal design theory is finding an experimental design that is optimal with respect to some criteria in a class of designs. The most popular criteria include the A- and D-criteria. Regular graph designs occur in many optimality results and, if the number of blocks is large enough, they are A- and D-optimal. We present the results of an exact computer search for the best regular graph designs in large systems for up to 20 points, k<=r<=10 and r(k-1)-(v-1)[r(k-1)/(v-1)]<=9.