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\footnotesize
\noindent Statistica Sinica {\bf 13}(2003), 403-408
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\centerline{\large\bf SOME PROPERTIES OF BLOCKED AND UNBLOCKED}
\vspace{2pt}
\centerline{\large\bf FOLDOVERS OF $2^{k-p}$ DESIGNS}
\vspace{.25cm}
\centerline{Kenny Q. Ye and William Li}
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\centerline{\it State University of New York at Stony Brook
%Stony Brook University
and University of Minnesota}
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\begin{quotation}
\noindent {\it Abstract:}
In this article, we focus on the theoretical properties of the
foldover design and the resulting combined design obtained by
augmenting an initial design by its foldover. We prove that there
are $2^p$ distinct ways to fold over a $2^{k-p}$ design. Optimal
foldover plans are also discussed. We investigate the impact of
the inclusion of a blocking variable to the design. We show that
the minimum aberration foldover design with the presence of the
blocking effect is the same as the one without blocking.\par
\vspace{9pt}
\noindent {\it Key words and phrases:}
Minimum aberration, optimal foldover, resolution,  word length pattern.\par
\end{quotation}
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