A survey of orthogonal arrays of strength two

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(₁ p,k ₁,p,2) and an orthogonal array (₂ p ²,k ₂,p,2) leads to another orthogonal array (₁₂ 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.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.