Balanced Sample Design On The District Team Leader For The Four-dimensional Non-adjacent Vertex Construction

Balanced sampling plans excluding contiguous units (BSEC) were Rrst introduced in 1988 by Hedayat, Rao and Stufken. These designs can be used in survey sampling when the contiguous units in some ordering provide similar information, such as estimates of population characteristics. Balanced sampling plans excluding contiguous units have two cases of one dimension and two dimension.In this paper, we study two dimensional BSECs with block size four in five parts. Firstly, we state the background, the basic definitions and some properties of BSECs. Secondly, we introduce some definitions and notations as well as preliminary results which will be used in the sequel. Thirdly, we show some recursive constructions for two dimensional BSECs with block size four. Fourthly, we give some direct constructions of small order. Finally, we show the existences of some infinite classes.