Constructions of Balanced Sampling Plan excluding Contiguous Units

Balanced sampling plan excluding contiguous units (or BSEC for short) was rst introduced by Hedayat, Rao and Stufken in 1988. These designs can be used for survey sampling when the units are arranged in one-dimensional ordering and the contiguous units in this ordering provide similar information. The properties and constructions of these objects were discussed in several papers, however, the existence problem of these designs is still widely opened. For example, no innnite class of such designs is known for xed block size k and xed. In this paper, we discuss the constructions of these designs in view of combinatorial design theory. Among other constructions, we use Langford sequence to construct all the possible BSEC with block size 3 and = 1, thus give the necessary and suucient conditions of such designs. Some constructions of BSA for xed , a generalization of BSEC, are also given. Then we generalize this concept to two-dimensional situation and give some constructions by using modiied group divisible designs. Some equivalent objects are mentioned.