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\footnotesize \noindent Statistica Sinica {\bf 21} (2011), 1453-1471

\vspace{3pc} \normalsize

\centerline{\large\bf A COSET PATTERN IDENTITY BETWEEN A  $2^{n-p}$}
\vspace{2pt} \centerline{\large\bf DESIGN AND ITS COMPLEMENT}
\vspace{.25cm}
\author{Peng Zeng$^1$, Hong Wan$^2$ and Yu Zhu$^2$}
\vspace{.4cm} \centerline{\it $^1$Auburn University and $^2$Purdue
University} \vspace{.55cm} 
\begin{quotation}
\noindent {\it Abstract:} The coset pattern matrix contains more
detailed information about effect aliasing in a factorial design
than the commonly used wordlength pattern. More flexible and
elaborate design criteria can be proposed using the coset pattern
matrix. In this article, we establish an identity that relates the
coset pattern matrix of a design to that of its complement. As an
application, the identity is used to characterize minimum
$M$-aberration designs through their complements.\par \vspace{9pt}
\noindent {\it Key words and phrases:} Complementary design, coset
pattern matrix, fractional factorial design, minimum $M$-aberration,
wordlength pattern. \par
\end{quotation}
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