E(s²)- and UE(s²)-optimal supersaturated designs

Supersaturated designs are useful for factor screening experiments under the factor sparsity assumption that only a small number of factors are active. The popular E(s²)-criterion for choosing two-level supersaturated designs minimizes the sum of squares of theentries of the information matrix over the designs in which the two levels of each factor appear equal number of times. Jones and Majumdar (2014) proposed the UE(s²)-criterion which is essentially the same as the E(s²)-criterion except that the requirement of factor-level-balance is dropped. Removing this constraint makes UE(s²)-optimal designs easy to construct, but it also produces many UE(s²)-optimal designs with diverse performances. It is necessary to choose better designs from them, especially those with good lower-dimensional projection properties. While E(s²)-optimal designs tend to have better lower-dimensional projections than arbitrary UE(s²)-optimal designs, they are usually very difficult to construct. We propose a secondary criterion and provide simple and systematic constructions of superior UE(s²)-optimal designs having good projection properties. We also derive conditions under which E(s²)-optimal designs are UE(s²)-optimal as well and identify several families of designs that are optimal under both criteria.