Abstract: Second order saturated (SOS) designs allow the estimation of a saturated model consisting of main effects and two-factor interactions. Apart from being useful in their own right, SOS designs have recently been applied to the construction of space-filling designs. This paper introduces the notion of minimal SOS designs to facilitate the study of SOS designs, and presents some results on the characterization and construction of minimal SOS designs. Both regular and nonregular minimal SOS designs are considered, and are applied to construct space-filling designs.

Key words and phrases: Clear effect, maximal design, nonregular design, space-filling design, strong orthogonal array.