Nested Partially Balanced Incomplete Block Design

Abstract

In this note we construct nested partially balanced incomplete block designs based on \(NC_{m}\)-scheme. Secondly we construct NPBIB designs from a given PBIB design with \(\lambda_{1} = 1\) and \(\lambda_{2} = 0\) with same association scheme for both systems of PBIB designs. Finally, we give some results and examples where the two systems of PBIB designs in NPBIB designs have different association schemes.