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Statistica Sinica 9(1999), 905-912



UNIFORM DESIGNS BASED ON LATIN SQUARES


Kai-Tai Fang, Wai-Chee Shiu and Jian-Xin Pan


Hong Kong Baptist University


Abstract: have been widely used in various fields. Traditionally they were generated by so-called good lattice point (glp) sets. In this paper, we propose a new approach based on cyclic Latin squares (CLS). The UDs generated have much smaller discrepancies than those proposed by Wang and Fang (1981). A threshold accepting algorithm is employed for finding the CLS with smallest $L_2$-discrepancy.



Key words and phrases: Experimental design, Latin squares, $L_2$-discrepancy, threshold accepting algorithm, uniform design, uniformity.


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