Construction of supersaturated design with large number of factors by the complementary design method

Supersaturated designs (SSDs) have been widely used in factor screening experiments. The present paper aims to prove that the maximal balanced designs are a kind of special optimal SSDs under the E(f _NOD) criterion. We also propose a new method, called the complementary design method, for constructing E(f _NOD) optimal SSDs. The basic principle of this method is that for any existing E(f _NOD) optimal SSD whose E(fNOD) value reaches its lower bound, its complementary design in the corresponding maximal balanced design is also E(f _NOD) optimal. This method applies to both symmetrical and asymmetrical (mixed-level) cases. It provides a convenient and efficient way to construct many new designs with relatively large numbers of factors. Some newly constructed designs are given as examples.