Two-level D- and A-optimal designs of Ehlich type with run sizes three more than a multiple of four

TL;DR

This paper develops an algorithm to generate and enumerate all non-isomorphic D- and A-optimal main-effects experimental designs for run sizes that are three more than a multiple of four, up to size 19.

Contribution

It introduces a novel algorithm to identify all optimal designs for specific run sizes previously unexplored, filling a gap in the design literature.

Findings

Enumerated all such designs for run sizes up to 19.

Identified designs that minimize aliasing among effects.

Provided counts of optimal designs for each run size.

Abstract

For the majority of run sizes N where N <= 20, the literature reports the best D- and A-optimal designs for the main-effects model which sequentially minimizes the aliasing between main effects and interaction effects and among interaction effects. The only series of run sizes for which all the minimally aliased D- and A-optimal main-effects designs remain unknown are those with run sizes three more than a multiple of four. To address this, in our paper, we propose an algorithm to generate all non-isomorphic D- and A-optimal main-effects designs for run sizes three more than a multiple of four. We enumerate all such designs for run sizes up to 19, report the numbers of designs we obtained, and identify those that minimize the aliasing between main effects and interaction effects and among interaction effects.