Uniform designs based on Latin squares

Kai Tai Fang; Wai Chee Shiu; Jian Xin Pan

Uniform designs based on Latin squares

Kai Tai Fang^*
, Wai Chee Shiu
, Jian Xin Pan

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

45 Citations (Scopus)

46 Downloads (Pure)

Abstract

Uniform designs (UDs) 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 L2-discrepancy.

Original language	English
Pages (from-to)	905-912
Number of pages	8
Journal	Statistica Sinica
Volume	9
Issue number	3
Publication status	Published - Jul 1999

User-Defined Keywords

Experimental design
L-discrepancy
Latin squares
Threshold accepting algorithm
Uniform design
Uniformity

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http://www3.stat.sinica.edu.tw/statistica/oldpdf/A9n315.pdf

Cite this

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title = "Uniform designs based on Latin squares",

abstract = "Uniform designs (UDs) 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 L2-discrepancy.",

keywords = "Experimental design, L-discrepancy, Latin squares, Threshold accepting algorithm, Uniform design, Uniformity",

author = "Fang, \{Kai Tai\} and Shiu, \{Wai Chee\} and Pan, \{Jian Xin\}",

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AU - Fang, Kai Tai

AU - Shiu, Wai Chee

AU - Pan, Jian Xin

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N2 - Uniform designs (UDs) 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 L2-discrepancy.

AB - Uniform designs (UDs) 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 L2-discrepancy.

KW - Experimental design

KW - L-discrepancy

KW - Latin squares

KW - Threshold accepting algorithm

KW - Uniform design

KW - Uniformity

UR - http://www3.stat.sinica.edu.tw/statistica/j9n3/j9n315/j9n315.htm

UR - https://www.jstor.org/stable/24306622

UR - https://www.scopus.com/pages/publications/0033459064

M3 - Journal article

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VL - 9

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EP - 912

JO - Statistica Sinica

JF - Statistica Sinica

IS - 3

ER -

Uniform designs based on Latin squares

Abstract

User-Defined Keywords

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