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<p>Association schemes come from the study of partially balanced incomplete block designs (PBIBDs) and are important in many fields. An array is schematic if its runs form an association scheme under a given distance, and such arrays are useful for experimental design and software test suite generation. However, existing research mainly focuses on the properties and constructions of schematic arrays, especially orthogonal arrays under the Hamming distance. There is little research on schematic arrays under other distances. It is hard to get explicit expressions of schematic design matrices under the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L_1\)</EquationSource> </InlineEquation> and Lee distance, and the construction of schematic Latin hypercube designs (LHDs) under these two distances is not well developed. The complexity of these two distances and schematic properties makes it difficult to derive explicit expressions and construct such schematic LHDs. This paper proposes several construction methods for schematic and revised schematic LHDs under the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L_1\)</EquationSource> </InlineEquation> and Lee distance, and provides examples to illustrate these methods.</p>

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Schematic latin hypercube designs

  • 期刊论文

  • 发表日期：

    2026年5月18日

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  • Zuolu Hao,
  • Yu Tang

摘要

Association schemes come from the study of partially balanced incomplete block designs (PBIBDs) and are important in many fields. An array is schematic if its runs form an association scheme under a given distance, and such arrays are useful for experimental design and software test suite generation. However, existing research mainly focuses on the properties and constructions of schematic arrays, especially orthogonal arrays under the Hamming distance. There is little research on schematic arrays under other distances. It is hard to get explicit expressions of schematic design matrices under the \(L_1\) and Lee distance, and the construction of schematic Latin hypercube designs (LHDs) under these two distances is not well developed. The complexity of these two distances and schematic properties makes it difficult to derive explicit expressions and construct such schematic LHDs. This paper proposes several construction methods for schematic and revised schematic LHDs under the \(L_1\) and Lee distance, and provides examples to illustrate these methods.