Equireplicate balanced block designs with nested rows and columns with at most two unequal block sizes

Abstract

Constructions are given for equireplicate balanced block designs with nested rows and columns with at most two unequal block sizes. Universal optimality of proposed designs are established under the usual homoscedastic fixed effects linear additive model. For v, the number of treatments, less than or equal to ten, a total of 115 equireplicate designs with at most two unequal block sizes are listed.