Construction of polygonal designs using linear integer programming

Abstract

This article proposes a new linear integer programming approach to obtain polygonal designs for given number of treatments v, block size k, concurrence of treatments separated by a distance of m + 1 or more as λ and all other concurrences as zero, m<=[v/2]. The main feature of the proposed approach is that it directly identifies the required incidence vectors for generating a polygonal design. Using the proposed approach, a complete solution is provided for constructing polygonal designs for number of treatments v ≤ 100, block size k = 3, λ = 1, 2 and m=1,2,...,[v/2].