On the construction and existence of a certain class of complete diallel cross designs

In this paper the construction and existence of complete diallel cross designs as nested balanced incomplete block (BIB) designs with sub-block size two are discussed. Two simple and general methods of constructing these designs using binary pairwise balanced designs and strongly equineighboured designs are given. Also, the necessary conditions for the existence of nested BIB designs with sub-block size two and super-block size four are found to be sufficient.