An asymptotic existence of balanced incomplete block (BIB) designs and pairwise balanced designs (PBD) has been discussed in [1]-[3]. On the other hand, the existence of additive BIB designs and pairwise additive BIB ...An asymptotic existence of balanced incomplete block (BIB) designs and pairwise balanced designs (PBD) has been discussed in [1]-[3]. On the other hand, the existence of additive BIB designs and pairwise additive BIB designs with k = 2?and?λ = 1?has been discussed with direct and recursive constructions in [4]-[8]. In this paper, an asymptotic existence of pairwise additive BIB designs is proved by use of Wilson’s theorem on PBD, and?also for some l?and k the exact existence of l?pairwise additive BIB designs with block size k and?λ = 1?is discussed.展开更多
A supersaturated design is a design whose run size is not enough for estimating all the main effects represented by the columns of the design matrix. It is widely used in the preliminary stages of industrial statistic...A supersaturated design is a design whose run size is not enough for estimating all the main effects represented by the columns of the design matrix. It is widely used in the preliminary stages of industrial statistics and other scientific experiments. In this paper, formulas for computing the E(s2) values of E(s2) optimal supersaturated designs with m = t(n - 1) ± e(e = 1 and 2) are given, and the accuracy and convenience of using these formulas are demonstrated by an example.展开更多
Association scheme is a structure on a finite set that has some special relations among elements in the set. These relations are usually hidden in other relations, so how to derive them out is a problem. The paper giv...Association scheme is a structure on a finite set that has some special relations among elements in the set. These relations are usually hidden in other relations, so how to derive them out is a problem. The paper gives a constructing method of mending parameters of the association schemes, and a new family of association schemes is obtained： quasiFmetric association scheme.展开更多
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
文摘An asymptotic existence of balanced incomplete block (BIB) designs and pairwise balanced designs (PBD) has been discussed in [1]-[3]. On the other hand, the existence of additive BIB designs and pairwise additive BIB designs with k = 2?and?λ = 1?has been discussed with direct and recursive constructions in [4]-[8]. In this paper, an asymptotic existence of pairwise additive BIB designs is proved by use of Wilson’s theorem on PBD, and?also for some l?and k the exact existence of l?pairwise additive BIB designs with block size k and?λ = 1?is discussed.
基金This research was supported by the NNSF project 19771049 of China
文摘A supersaturated design is a design whose run size is not enough for estimating all the main effects represented by the columns of the design matrix. It is widely used in the preliminary stages of industrial statistics and other scientific experiments. In this paper, formulas for computing the E(s2) values of E(s2) optimal supersaturated designs with m = t(n - 1) ± e(e = 1 and 2) are given, and the accuracy and convenience of using these formulas are demonstrated by an example.
文摘Association scheme is a structure on a finite set that has some special relations among elements in the set. These relations are usually hidden in other relations, so how to derive them out is a problem. The paper gives a constructing method of mending parameters of the association schemes, and a new family of association schemes is obtained： quasiFmetric association scheme.
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.
