Generalized polygonal designs with block size 3 and

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.