Optimality of Mixed-level Supersaturated Designs 
Shu Yamada and Tomomi Matsui 
METR 98-05,  April 1998 

Shu Yamada
Department of Management Science
Science University of Tokyo
Kagurazaka 1-3, Shinjuku, Tokyo 162-8601, Japan 
Tel +81 3 3260 4271, ext 3336 
Fax +81 3 3235 6479
e-mail: shu@ms.kagu.sut.ac.jp

Tomomi Matsui 
Department of Mathematical Engineering and Information Physics 
Faculty of Engineering
University of Tokyo
Hongo 7-3-1, Bunkyo, Tokyo 113-8656,  Japan
Tel +81 3 3812 2111 ext.6921
Fax + 81 3 5689 7358
e-mail: tomomi@misojiro.t.u-tokyo.ac.jp

\begin{abstract}
Supersaturated design is an important aspect
of experimental design.
Several properties of supersaturated designs have been obtained
that enable supersaturated design to be constructed
while maintaining low dependency
over all pairs of columns.
This paper presents generalized theorems on
the optimality of supersaturated designs.
Mixed-level supersaturated designs
are generated using a construction
method based on these theorems.
An index is proposed for measuring
the efficiency of supersaturated design
and is applied to the constructed mixed-level supersaturated designs.

\end{abstract}

Key words and phrases: $\chi^2$ statistic, dependency between two columns,
saturated and orthogonal design, lower bound of dependency 
AMS 1991 subject classifications: Primary 62K15, Secondary 05B20