Two-level D- and A-optimal main-effects designs with run sizes one and two more than a multiple of four

TL;DR

This paper develops algorithms to generate all optimal main-effects designs for certain run sizes, specifically those one or two more than a multiple of four, and compares these designs with existing benchmarks.

Contribution

It introduces two algorithms to enumerate all non-isomorphic D- and A-optimal designs for specific run sizes and identifies minimally aliased designs among them.

Findings

Enumerated all such designs up to run size 18.

Identified designs that minimize aliasing.

Compared these designs with existing benchmarks.

Abstract

For run sizes that are a multiple of four, the literature offers many two-level designs that are D- and A-optimal for the main-effects model and minimize the aliasing between main effects and interaction effects and among interaction effects. For run sizes that are not a multiple of four, no conclusive results are known. In this paper, we propose two algorithms that generate all non-isomorphic D- and A-optimal main-effects designs for run sizes that are one and two more than a multiple of four. We enumerate all such designs for run sizes up to 18, report the numbers of designs we obtained, and identify those that minimize the aliasing between main effects and interaction effects and among interaction effects. Finally, we compare the minimally aliased designs we found with benchmark designs from the literature.