New results in the packing of equal circles in a square
Discrete Mathematics
Finding elliptic Fekete points sets: two numerical solution approaches
Journal of Computational and Applied Mathematics
Learning from Data: Concepts, Theory, and Methods
Learning from Data: Concepts, Theory, and Methods
Efficient Global Optimization of Expensive Black-Box Functions
Journal of Global Optimization
Design and Analysis of Experiments
Design and Analysis of Experiments
Maximin Latin Hypercube Designs in Two Dimensions
Operations Research
Bounds for Maximin Latin Hypercube Designs
Operations Research
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The design of computer experiments is an important step in black-box evaluation and optimization processes. 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 are particularly useful as training and test sets for fitting and validating metamodels, respectively. Furthermore, nested designs can be used to deal with linking parameters and sequential evaluations. In this paper, we introduce one-dimensional nested maximin designs. We show how to nest two designs optimally and develop a heuristic to nest three and four designs. These nested maximin designs can be downloaded from the website http://www.spacefillingdesigns.nl . Furthermore, it is proven that the loss in space-fillingness, with respect to traditional maximin designs, is at most 14.64 and 19.21%, when nesting two and three designs, respectively.