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A supersaturated design (SSD) is a factorial design whose run size is not enough for estimating all the main effects. Such designs have received much recent interest because of their potential in factor screening experiments. This paper first shows that the design obtained by the Kronecker sum of a balanced design and a generalized Hadamard matrix (i.e., a matrix with both itself and its transpose being difference matrices) has some nice properties. Based on these findings, some new methods for constructing-optimal SSDs via generalized Hadamard matrices are developed. Meanwhile, the non-orthogonality of the proposed designs is well controlled by the source designs. In addition, some generalized Hadamard matrices with nice properties are constructed for obtaining-optimal SSDs. The proposed methods are easy to implement and many new SSDs can then be constructed.

Construction of optimal supersaturated designs via generalized Hadamard matrices