  Efficient Latin hypercube designs (LHDs), including maximin distance LHDs,
maximum projection LHDs and orthogonal LHDs, are widely used in computer
experiments. It is challenging to construct such designs with flexible sizes,
especially for large ones. In the current literature, various algebraic methods
and search algorithms have been proposed for identifying efficient LHDs, each
having its own pros and cons. In this paper, we review, summarize and compare
some currently popular methods aiming to provide guidance for experimenters on
what method should be used in practice. Using the R package we developed which
integrates and improves various algebraic and searching methods, many of the
designs found in this paper are better than the existing ones. They are easy to
use for practitioners and can serve as benchmarks for the future developments
on LHDs.
