One Dimensional Balanced Sampling Plan Excluding Contiguous Units With Block Size Five

Hedayat, Rao and Stufken first introduced balanced sampling plan excluding contiguousunits(BSEC)in1988. Just as the estimating of population characteristics and the evaluating ofenvironments, which the contiguous units provide similar information, the idea of BSEC be-comes particularly suitable. The ordering of BSEC can be divided into two conditions, whichare one dimensional and two dimensional. We mainly study one dimensional BSEC (1-BSEC)with block size five into four parts in this paper. First, we introduce the background, the formaldefinitions of BSEC and some known results. In the second part, we introduce some related de-signs such as group divisible design, incomplete orthogonal latin square and incomplete groupdivisible design, at the same time we also give some results about their existence. Then we givesome direct constructions of small order, which are extremely important at the later recursiveconstructions. In the forth part, we demonstrate two classes on the existence of1-BSEC in thecase of k=5, λ=1, at the same time we give the result of1-BSEC when k=5and λ=4with one possibly exception.