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\footnotesize \noindent Statistica Sinica {\bf 19} (2009), 1705-1719

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 \centerline{\large\bf CONSTRUCTION OF MIXED-LEVEL SUPERSATURATED}
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 \centerline{\large\bf DESIGNS BY THE SUBSTITUTION METHOD}
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 \author{Min-Qian Liu and Zhao-Yang Cai}
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 \centerline{\it Nankai University}
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\begin{quotation}
\noindent {\it Abstract:} Supersaturated design (SSD) has received
much interest because of its potential in factor screening
experiments. Most studies focus on the construction and analysis of
symmetrical SSDs. This paper considers the construction of
asymmetrical (or mixed-level) SSDs. A new construction method,
called the substitution method, for $E(f_{_{NOD}})$ optimal and
nearly-optimal SSDs is proposed. The basic idea of this method is to
divide the rows of one design into several blocks, and then
substitute the levels of another design with these blocks. The two
designs can be SSDs and saturated orthogonal arrays, and their
selections are investigated in detail. The properties of the designs
generated are also discussed, and many new designs are tabulated for
practical use. \par
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 \noindent
{\it Key words and phrases:} Coincidence number, equidistant design,
mixed-level, orthogonal array, supersaturated design.
\par
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