Robert Mee, University of Tennessee

• Title: Two-level parallel flats designs

• Abstract: Regular $2^(n-p)$ designs are also known as single flat designs. Parallel flats designs (PFDs) consisting of three parallel flats (3-PFDs) are the most frequently utilized PFDs, due to their simple structure. Generalizing to $f$-PFD with $f > 3$ is more challenging. This talk summarizes recent work on a general theory for the $f$ -PFD for any $f \ge 3$. We propose a method for obtaining the confounding frequency vectors for all nonequivalent $f$-PFDs, and to find the least $G$-aberration (or highest D-efficiency) $f$ -PFD constructed from any single flat. We also characterize the quaternary code design series as PFDs. Finally, we show how designs constructed by concatenating regular fractions from different families may also have a parallel flats structure. Examples are given throughout to illustrate the results.