Construction of E (f_NOD)-Optimal Supersaturated Designs VIA Room Squares

Supersaturated design is essentially a fractional factorial in which the number of potential effects is greater than the number of runs. And Room square is an important object in combinatorial design theory. We show a link between these two apparently unrelated kinds of designs. E (f_NOD) criterion for comparing supersaturated designs is proposed and a lower bound of E (f_NOD) is obtained as a benchmark of design optimality. It is shown that the E (f_NOD) criterion is an extension of the popular E(s²) and ave x² criterion (for two- and three-level supersaturated designs respectively). A new construction method for multi-level supersaturated designs via Room squares is also proposed and some properties of the resulting designs are investigated.