Supersaturated design (SSD) has received much recent interest because of its potential in factor screening experiments. In this paper, we provide equivalent conditions for two columns to be fully aliased and consequently propose methods for construct
ing $E(f_{mathrm{NOD}})$- and $chi^2$-optimal mixed-level SSDs without fully aliased columns, via equidistant designs and difference matrices. The methods can be easily performed and many new optimal mixed-level SSDs have been obtained. Furthermore, it is proved that the nonorthogonality between columns of the resulting design is well controlled by the source designs. A rather complete list of newly generated optimal mixed-level SSDs are tabulated for practical use.
We define the holomorphic Fourier transform of holomorphic functions on complex reductive groups, prove some properties like the Fourier inversion formula, and give some applications. The definition of the holomorphic Fourier transform makes use of t
he notion of $K$-admissible measures. We prove that $K$-admissible measures are abundant, and the definition of holomorphic Fourier transform is independent of the choice of $K$-admissible measures.
