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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.

Construction and existence of constant block sum PBIB designs