Abstract: We consider screening experiments where an investigator wishes to study many factors using fewer observations. Our focus is on experiments with two-level factors and a main effects model with intercept. Since the number of parameters is larger than the number of observations, traditional methods of inference and design are unavailable. In 1959, Box suggested the use of supersaturated designs and in 1962, Booth and Cox introduced measures for efficiency of these designs including E(s2), which is the average of squares of the off-diagonal entries of the information matrix, ignoring the intercept. For a design to be E(s2)-optimal, the main effect of every factor must be orthogonal to the intercept (factors are balanced), and among all designs that satisfy this condition, it should minimize E(s2). This is a natural approach since it identifies the most nearly orthogonal design, and orthogonal designs enjoy many desirable properties including efficient parameter estimation. Factor balance in an E(s2)-optimal d...