The Existence Of A Class Of One Dimensional Balanced Sampling Plan Excluding Contiguous Units With Block Size Five

The balanced sampling plan excluding contiguous units(BSEC) was first introduced by Hedayat, Rao and Stufken in 1988[11]. Just as the estimating of population characteristics and the evaluating of environments, which the contiguous units provide similar information, the idea of BSEC becomes particularly suitable. The ordering of BSEC can be divided into two conditions, which are one dimensional and two dimensional.In this paper, we mainly study the constructions and the existence of one dimensional BSEC with block size five into four chapters.Chapter 1 In this chapter, we mainly introduce the background, the formal definitions of BSEC and some known results.Chapter 2 We introduce some related designs such as group divisible design, incomplete group divisible design and give some results of their existence.Chapter 3 Applying some designs on small orders, we obtain the existence of 1-BSEC(v, 5, λ) directly.Chapter 4 Applying GDD, IGDD and some known constructions, we obtain the constructions of 1-BSEC, and apply the constructions of 1-BSEC, we obtain some recursive constructions of 1-BSEC and some results of 1-BSEC with block size five.The main result are:(1) Let v ≡ 0, 3(mod 5), and v ≥ 18, there exists a 1-BSEC(v, 5, 4).(2) Let v ≡ 3(mod 10), and v ≥ 23, we give the result of 1-BSEC(v, 5, 10), except possibly for v = {163, 173, 183, 193, 213, 223, 283, 393, 403}.(3) Let v ≡ 5(mod 10), and v ≥ 25, there exists a 1-BSEC(v, 5, 10).