A cyclic construction of saturated and supersaturated designs

Supersaturated design (SSD) has received much interest because of its potential in factor screening experiments. Inspired by the construction of cyclic orthogonal designs with prime power run numbers in Plackett and Burman (1946), a method for constructing χ2(D) optimal multi-level SSDs with cyclic structure is explored in this paper. Some newly constructed designs are tabulated for practical use. Meanwhile, some of the resulting designs are shown to be also optimal under the maxχ2 criterion. In addition, we show that a sufficient condition for a balanced mixed-level saturated design to be orthogonal is that the weighted coincidence number between any two distinct rows of this design is a constant. An easier proof for the orthogonality of the Plackett and Burman designs with prime power run numbers is also presented.