Construction of Tm-type and Tm-assisted PBIB designs

Abstract

Two-associate class triangular designs have been explored greatly but the Tm-type PBIB designs (m ≥ 3) largely remains unexplored. The paper is written with an objective to construct a new series of Tm-type PBIB designs and to derive some more series of PBIB designs based on these PBIB designs, which we have called as Tm-assisted PBIB designs. For this, we begin by first constructing a series of Tm-type PBIB designs and then based on these designs, three series of Tm-assisted PBIB designs have been constructed. The association schemes of Tm-type and Tm-assisted PBIB designs have been discussed in their complete generalized form.

Keywords

• Block designs
• triangular association scheme
• PBIB designs