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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