Generalized polygonal designs with block size 3 and λ=1

Polygonal designs are useful in survey sampling in terms of balanced sampling plans excluding contiguous or adjacent units, when neighboring units in a population provide similar information. In this paper, we consider the construction of polygonal designs for generalized distance m with block size 3 and λ=1 by using the method of cyclic shifts. The distinguishing feature of this method is that the properties of a design can easily be obtained from the sets of shifts instead of constructing the actual blocks of the design. The pattern of zero-off-diagonal elements from the main-diagonal in a concurrence matrix is useful in the identification of the distance in a polygonal design. A catalog of generalized polygonal designs with k=3 and λ=1 for generalized distance 1⩽m⩽[(v-1)/2] and v∈{9,15,…,99} is compiled.