Abstract: Latin hypercube designs have been widely used in computer experiments with quantitative factors. When there are both qualitative and quantitative factors in computer experiments, sliced space-filling designs have been proposed. In this article, we propose a general framework for constructing sliced space-filling designs for more flexible parameters of designs in which the whole design and each slice not only achieve maximum stratification in univariate margins, but also achieve stratification in two- or more-dimensional margins. Compared with other designs, these designs have better space-filling properties or have more columns. The construction is based on a new class of sliced orthogonal arrays, called balanced sliced orthogonal arrays, in which each slice is balanced and becomes an orthogonal array after some level-collapsing. Several approaches to constructing such balanced sliced orthogonal arrays under different level-collapsing projections are developed. Some examples are given to illustrate the construction methods.

Key words and phrases: Balanced, computer experiment, difference matrix, Latin hypercube design, sliced orthogonal array, sliced space-filling design.