Some new classes of orthogonal Latin hypercube designs

Enumeration and Evaluation of Small Orthogonal Latin Hypercube Designs for Polynomial Regression Models

“…These small designs can also be used as building blocks for forming designs with more runs, following the stacking methods of Lin, Bingham, Sitter and Tang and of Ai, He, and Liu, or the methods that use Orthogonal Arrays of Lin, Mukerjee and Tang and Dey and Sarkar . For example, using the two nonisomorphic designs of the set O L H D 3 (8,4) and the three nonisomorphic designs of the set O L H D 3 (9,4), we can generate 2·4!·2 4 ·3·4!·2 4 orthogonal Latin hypercubes with n = 17 runs and k = 4 columns, which are classified in 156 nonisomorphic classes that belong to the set O L H D 3 (17,4).…”

“…Much work has been preformed in the literature to establish efficient methods for constructing orthogonal Latin hypercubes. Much attention has been given to the construction of orthogonal Latin hypercubes that belong to the set O L H D 3 ( n , k ) and guarantees no correlation between the estimates of the first‐order effects and between the estimates of the first‐order effects with the estimates of the second‐order effects, see Lin, Lin, Bingham, Sitter and Tang, Ye, Butler, Steinberg and Lin, Cioppa and Lucas, Bingham, Sitter and Tang, Georgiou, Georgiou and Stylianou, Lin, Mukerjee and Tang, Pang, Liu and Lin, Sun, Liu and Lin, Ai, He and Liu, Yang and Liu, Dey and Sarkar, and of Georgiou and Efthimiou among others. However, to the best of our knowledge, the field of design evaluation and optimal selection for Latin hypercubes with given n and k via complete enumeration of nonisomorphic designs remains poorly explored in the literature (see Lin, p. 31).…”

New bounds and search for maximin distance U‐type designs

“…In computer experiments, U‐type designs with good space‐filling properties, such as Latin hypercube designs and orthogonal arrays, are commonly used (Bingham et al, 2009; Lin & Tang, 2015). Various criteria have been put forth for optimizing space‐filling properties of U‐type designs, including the widely used maximin distance criterion (Johnson et al, 1990; Morris & Mitchell, 1995), the column orthogonality criterion (Ai et al, 2012; Bingham et al, 2009), the uniformity criterion (Fang et al, 2006) and the maximum projection criterion (Joseph et al, 2015), etc. For an exhaustive review, we refer the reader to Lin and Tang (2015).…”