Nested Maximin Latin Hypercube Designs in Two Dimensions

In black box evaluation and optimization Latin hypercube designs play an important role.When dealing with multiple black box functions the need often arises to construct designs for all black boxes jointly, instead of individually.These so-called nested designs consist of two separate designs, one being a subset of the other, and are used to deal with linking parameters and sequential evaluations.In this paper we construct nested maximin designs in two dimensions.We show that different types of grids should be considered when constructing nested designs and discuss how to determine which grid to use best for a specifc computer experiment.In the appendix to this paper maximin distances for different numbers of points are provided; the corresponding nested maximin designs can be found on the website http://www.spacefillingdesigns.nl.