Constructions of Sarvate-Beam Group Divisible Designs

TL;DR

This paper establishes the existence of a Sarvate-Beam variant of group divisible designs with uniform block size three, expanding the understanding of complex combinatorial design structures.

Contribution

It introduces and proves the existence of a new class of Sarvate-Beam group divisible designs of uniform type with block size three.

Findings

Existence of Sarvate-Beam group divisible designs proven

Extension of combinatorial design theory achieved

New design structures characterized and constructed

Abstract

A balanced incomplete block design is a set system in which all pairs of distinct elements occur with a constant frequency. By contrast, a Sarvate-Beam design induces an interval of distinct frequencies on pairs. In this paper, we settle the existence of a Sarvate-Beam variant of group divisible designs of uniform type with block size three.