A1192
Title: Construction of space-filling Latin hypercube designs with flexible run sizes
Authors: Sixu Liu - Yanqi Lake Beijing Institute of Mathematical Sciences and Applications (China) [presenting]
Yaping Wang - East China Normal University (China)
Qian Xiao - Shanghai Jiaotong University (China)
Abstract: The purpose is to study using Williams transformed good lattice point (GLP) sets to construct space-filling Latin hypercube designs (LHDs) of size $n\phi(n)$, where $\phi(n)$ is the Euler function and $n=pq$ for distinct primes $p$ and $q$. Williams transformed GLP sets have recently been shown as a powerful tool for constructing maximin L1-distance LHDs. However, the existing theoretical results only cover the cases of $n=p$ and $n=2p$. The optimality results for more general sizes of n=pq are shown, where p and q can be any two distinct prime numbers. A simple representation of such GLP designs is derived and used to prove their asymptotic optimality under the maximin L1-distance criterion. A method is also proposed to construct more space-filling LHDs with flexible sizes based on Williams-transformed GLP designs.
