Contributions to Factorial Designs and Space-Filling Designs

In physical and computer experiments, factorial designs and space-filling designs are frequently employed to explore the relationship between several input factors and a response variable. Several new developments for these designs are documented in this thesis. Generalized resolution, projectivity, and hidden projection property are useful measures to evaluate a factorial design, especially when only a few factors are believed to be active a priori. In this thesis, we substantially expand existing theoretical results on these topics by examining designs from Paley's constructions of Hadamard matrices. Next, we study two-level factorial experiments where the two levels are symmetrical for some factors but asymmetrical for other factors. A mixed parametrization of factorial effects is proposed for such situations. For robust estimation of main effects, we introduce two minimum aberration criteria and provide theoretical and algorithmic constructions of optimal and nearly optimal designs under these criteria. Space-filling designs based on orthogonal arrays are attractive for computer experiments. However, it's not very clear how they perform under other space-filling criteria. In this thesis, we justify the use of these designs under a broad class of space-filling criteria including those of distance, orthogonality and discrepancy. Based on the theoretical results, we investigate various constructions of space-filling orthogonal array-based designs. Finally, we develop a construction method of space-filling designs using nonregular designs. Designs obtained this way have very flexible run sizes as compared to those constructed from regular designs.