Construction and existence of constant block sum PBIB designs

Abstract

The present article proposes three series of partially balanced incomplete constant block sum designs constructed using regular graphs. Two series develop a three-associate class PBIB designs and one develops a five-associate class PBIB design. Moreover, we were able to show the existence of constant block sum PBIB designs with their parameters for a specified association scheme. Towards the end, we have discussed few possible designs, the blocks of which may be constructed from the association schemes discussed in the present research paper.

Keywords:

• Constant block sum partially balanced incomplete block designs
• regular graphs
• balanced incomplete block designs

Acknowledgments

We are thankful to the reviewers for their suggestions which made the manuscript more informative, valuable and presentable.