Rotated sphere packing designs

TL;DR

This paper introduces rotated sphere packing designs, a new class of space-filling designs for computer experiments that optimize coverage, uniformity, and prediction accuracy, with a fast construction algorithm and supporting theoretical and numerical evidence.

Contribution

It presents a novel design method based on sphere packing principles, offering improved space-filling properties and a practical algorithm for various dimensions and sample sizes.

Findings

Excellent maximin distance and low discrepancy.

Good projective uniformity for prediction and integration.

Efficient construction algorithm available online.

Abstract

We propose a new class of space-filling designs called rotated sphere packing designs for computer experiments. The approach starts from the asymptotically optimal positioning of identical balls that covers the unit cube. Properly scaled, rotated, translated and extracted, such designs are excellent in maximin distance criterion, low in discrepancy, good in projective uniformity and thus useful in both prediction and numerical integration purposes. We provide a fast algorithm to construct such designs for any numbers of dimensions and points with R codes available online. Theoretical and numerical results are also provided.