OPTIMAL INCOMPLETE BLOCK-DESIGNS FOR GENERAL DEPENDENCE STRUCTURES

The paper introduces strongly equineighboured designs, which are relevant designs for the usual case of dependent observations which have a centrosymmetric dispersion matrix. The designs are shown to be weakly universally optimal BIB designs under ordinary least-squares for any dependence structure. They are also shown to be universally optimal binary designs under generalized least-squares for any dependence structure, and optimal over all designs for some dependence structures. Some other designs are considered for the cases when the strongly equineighboured designs are not optimal. The results unify previous work on this topic.