A method for constructing supersaturated designs and its Es² optimality

A lower bound for the Es 2 value of an arbitrary supersaturated design is derived. A general method for constructing supersaturated designs is proposed and shown to produce designs with n runs and m = k ( n — 1) factors that achieve the lower bound for Es 2 and are thus optimal with respect to the Es 2 criterion. Within the class of designs given by the construction method, further discrimination can be made by minimizing the pairwise correlations and using the generalized D and A criteria proposed by Wu (1993). Efficient designs of 12, 16, 20 and 24 runs are constructed by following this approach.