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 set D(2p.2p,p,2), where p is a prime or a prime power, ar...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 set D(2p.2p,p,2), where p is a prime or a prime power, are given. It is shown that the Kronecker sum of a difference set D(λ1p, k1, p, 2) and an orthogonal array(λ2p2, k2, p, 2) leads to another orthogonal array (λ1λ2p3 .k1k2+1 ,p, 2). This enables us to construct orthogonal arrays[2p(n+1)、1+2(p+p2 +…+pn),p,2],[4p(n+2),1+2p+4(p2+p3+…+p(n+1)),p, 2],and [8p(n+3),1+2P+4p2+8(p3+p4+…+p(n+2)),p,2]where p is a prime or a prime power.展开更多
In this paper a new class of orthogonal arrays(OAs),i.e.,OAs without interaction columns,are proposed which are applicable in factor screening,interaction detection and other cases.With the tools of difference matrice...In this paper a new class of orthogonal arrays(OAs),i.e.,OAs without interaction columns,are proposed which are applicable in factor screening,interaction detection and other cases.With the tools of difference matrices,we present some general recursive methods for constructing OAs of such type.Several families of OAs with high percent saturation are constructed.In particular,for any integerλ≥3,such a two-level OA of run 4λcan always be obtained if the corresponding Hadamard matrix exists.展开更多
文摘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 set D(2p.2p,p,2), where p is a prime or a prime power, are given. It is shown that the Kronecker sum of a difference set D(λ1p, k1, p, 2) and an orthogonal array(λ2p2, k2, p, 2) leads to another orthogonal array (λ1λ2p3 .k1k2+1 ,p, 2). This enables us to construct orthogonal arrays[2p(n+1)、1+2(p+p2 +…+pn),p,2],[4p(n+2),1+2p+4(p2+p3+…+p(n+1)),p, 2],and [8p(n+3),1+2P+4p2+8(p3+p4+…+p(n+2)),p,2]where p is a prime or a prime power.
基金supported by NSFC grants 11971004 and 11571094supported by NSFC grants 11901199 and 71931004+2 种基金supported by NSFC grants 12071014 and 12131001Shanghai Sailing Program 19YF1412800SSFC grant 19ZDA121 and LMEQF。
文摘In this paper a new class of orthogonal arrays(OAs),i.e.,OAs without interaction columns,are proposed which are applicable in factor screening,interaction detection and other cases.With the tools of difference matrices,we present some general recursive methods for constructing OAs of such type.Several families of OAs with high percent saturation are constructed.In particular,for any integerλ≥3,such a two-level OA of run 4λcan always be obtained if the corresponding Hadamard matrix exists.
