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A survey of orthogonal arrays of strength two

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Abstract

The purpose of this paper is to survey the construction of orthogonal arrays of strength two by using difference sets. Some methods for constructing difference setD(2p,2p,p,2), wherep is a prime or a prime power, are given. It is shown that the Kronecker sum of a difference setD(λ1 p,k 1,p,2) and an orthogonal array (λ2 p 2,k 2,p,2) leads to another orthogonal array (λ1λ2 p 3,k 1 k 2+1,p,2). This enables us to construct orthogonal arrays [2p n+1, 1+2(p+p 2+...+p n,p),2], [4p n+2, 1+2p+4(p 2+p 3+...+p n+1),p,2], and [8p n+3, 1+2p+4p 2+8(p 3+p 4+...+p n+2),p,2] wherep is a prime or a prime power.

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Authors and Affiliations

  1. Institute of Applied Mathematics, the Chinese Academy of Sciences, 100080, Beijing, China

    Liu Zhangwen

  2. Okayama University of Science, 700, Japan

    Fujii Yoshio

  3. International Institute for Natural Sciences, 710, Kurashiki, Japan

    Fujii Yoshio

Authors
  1. Liu Zhangwen
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  2. Fujii Yoshio
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Additional information

This work was carried out while the author was a visiting professor at the International Institute for Natural Sciences, Kurashiki 710 Japan, during Oct. 1990-July 1991.

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Liu, Z., Yoshio, F. A survey of orthogonal arrays of strength two. Acta Mathematicae Applicatae Sinica 11, 308–317 (1995). https://doi.org/10.1007/BF02011197

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  • DOI: https://doi.org/10.1007/BF02011197

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