Two-dimensional Balanced Sampling Plans Excluding Contiguous Units With Block Size Five

The balanced sampling plans excluding contiguous units (BSEC) was first proposed by Hedayat, Rao and Stufken in 1988. The design is commonly used in sample surveys of some contiguous units that may provide similar information. The sample points order of BSEC is divided into two kinds of orderly sequence, one is one-dimensional, the other is two-dimensional. The main research of this paper is two-dimensional balanced sampling plans excluding contiguous units (2-BSEC) with block size five. The paper is divided into four parts introduced. The first part is the background of BSEC. And the second part is the first chapter, which gives the basic concepts and some known results of one-dimensional and two-dimensional BSEC. At the same time, which introduces some related designs and nature, such as group divisible design, incomplete group divisible design, group divisible design with equal-sized holes and modified group divisible design. The third part is the second chapter, which gives some Recursive Construction Methods of 2-BSEC. The last part is the third chapter, by using the methods that introduced by chapter two, we get some results of k= 5 and index of one, two and four. At the same time, it is provided that 2-BSEC(2,5,5, λ) and 2-BSEC(3,5,5, λ) doesn:t exist.