Further results os the connectedness and Optimalityof designs of type O:XB

Abstract

This paper extends the work of Russell (1976). Proof Is given that, for many parameter sets, all O:XB designs belonging to the set are connected. It is shown how an (M,S)-optinal design nay be selected from the M-optimal designs of a given parameter set. The efficiencies of these (M,S)-optimal designs are displayed, and it is concluded that the (M,S)-optimality criterion is useful for selecting designs of high efficiency.

Keywords:

• balanced incomplete block design
• efficiency
• M-optimality
• (M,S)-optimality
• systems of direct representatives