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\footnotesize \noindent Statistica Sinica {\bf 19} (2009), 1721-1728

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\normalsize
 \centerline{\large\bf A CONSTRUCTION METHOD FOR ORTHOGONAL LATIN}
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 \centerline{\large\bf HYPERCUBE DESIGNS WITH PRIME POWER LEVELS}
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 \author{Fang Pang$^1$, Min-Qian Liu$^1$ and Dennis K. J. Lin$^2$}
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 \centerline{\it $^1$Nankai University and $^2$The Pennsylvania State University}
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\begin{quotation}
\noindent {\it Abstract:} Latin hypercube design (LHD) is popularly
used in designing computer experiments. This paper explores how to
construct LHDs with $p^d$ ($d=2^c$) runs and up to $(p^d-1)/(p-1)$
factors in which all main effects are orthogonal. This is
accomplished by rotating groups of factors in a  $p^d$-run regular
saturated factorial design. These rotated factorial designs are easy
to construct and preserve many attractive properties of standard
factorial designs. The proposed method covers the one by Steinberg
and Lin (2006) as a special case and is able to generate more
orthogonal LHDs with attractive properties. Theoretical properties
as well as the construction algorithm are discussed, with an example
for illustration. \par
 \vspace{9pt}
 \noindent
{\it Key words and phrases:} Computer experiment, factorial design,
galois field, rotation.
\par
\end{quotation}

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