Abstract: This paper uses orthogonal arrays to define generalizations of Latin hypercube sampling and of lattice sampling in the d dimensional unit cube. These are proposed as suitable designs for computer experiments, numerical integration and visualization. The orthogonal array based designs extend to t dimensional margins the univariate stratification properties of Latin hypercube and lattice sampling. As a consequence, the variance reduction property of Latin hypercube and lattice sampling. As a consequence, the variance reduction property of Latin hypercube and lattice sampling also extends to orthogonal array based samples. We give a sample based estimate of the error variance in the case of bivariate stratification.
Key words and phrases: Monte Carlo, variance reduction, quadrature.