Abstract: Tang and Wu (1997) derived a lower bound on the E(S2)-value of an arbitrary supersaturated design, and described a method of constructing some E(S2)-optimal designs achieving this lower bound. In this paper, we relate designs achieving Tang and Wu's bound to orthogonal arrays, and give a unified treatment of Tang and Wu's optimality result and the optimality of Lin's (1993) half Hadamard matrices. The optimality of designs obtained by adding one or two factors to (or by removing one or two factors from) those achieving Tang and Wu's bound is also proved. As an application, we give a complete solution of E(S2)-optimal 8-run designs which can accommoda te 8 to 35 factors.
Key words and phrases: Balanced incomplete block design, Hadamard matrix, Nearly balanced incomplete block design, orthogonal array.