Space-filling designs are commonly used in computer experiments aiming to build statistical surrogate models. In this thesis, we propose a minimum aberration type criterion and the stratified L_2-discrepancy for evaluating space-filling properties of designs based on design stratification properties on various grids. The idea of stratification comes from the stratified orthogonality of strong orthogonal arrays. The space-filling criterion provides a systematic way of classifying and ranking space-filling designs including various types of strong orthogonal arrays and Latin hypercube designs according to the space-filling hierarchy principle. Strong orthogonal arrays of maximum strength are favorable under the proposed space-filling criterion. The stratified L_2-discrepancy assesses the projection properties of designs based on points stratification properties and can be tuned flexibly. Projection uniformity is considered with respect to all possible stratifications with proper weights. The stratified L_2-discrepancy includes the space-filling criterion as a special case and is suitable for evaluating all kinds of designs with little curse of dimensionality. We further derive lower bounds for the stratified L_2-discrepancy and the space-filling pattern enumerator via defining a metric space that reveals the distance between points based on stratification. We show that generalized Hadamard matrices achieve the lower bounds and present a simple way to construct generalized Hadamard matrices via Galois fields. Comparisons between the optimal designs and other space-filling designs are illustrated.