  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.
