Construction of maximin distance Latin squares and related Latin hypercube designs

• 成果类型: Article
• 署名作者: Xiao, Qian; Xu, Hongquan
• 署名单位: University of California System; University of California Los Angeles
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asx006
• 发表日期: 2017
• 页码: 455464
• 关键词: computational experiments; costas arrays

摘要

Maximin distance Latin hypercube designs are widely used in computer experiments, yet their construction is challenging. Based on number theory and finite fields, we propose three algebraic methods to construct maximin distance Latin squares as special Latin hypercube designs. We develop lower bounds on their minimum distances. The resulting Latin squares and related Latin hypercube designs have larger minimum distances than existing ones, and are especially appealing for high-dimensional applications.