The Efficiency and Optimality Characterization of Certain Six-Treatment BIBDs emanating from some Quasi-semi-Latin squares

Polycarp Chigbu (University of Nigeria, Nigeria)

Balanced incomplete-block designs (BIBDs) were constructed from three types of three-factor block-structured combinatorial designs which are not necessarily semi-Latin squares but whose treatments are ab initio arranged as in the semi-Latin square. The basic consideration for the construction involves the exploitation of the different block structures of the experimental units of the Quasi-semi-Latin squares (QSLS) for the same treatments which are, herein, six in number. All the emanating designs are found to be connected; only the designs in nine blocks are both variance- and efficiency-balanced and offer gain in efficiency but lead to about 46 percent loss of information.