Construction of Equi-replicated Balanced Block Designs with Block Sizes Exceeding the Number of Treatments

In this note it is shown that the block design with incidence matrix Ñ = NN… N], where N = c_1hN_h + c_oh (11′–N_h). c_oh and c_1h are any non-negative integers and N_h,h = 1, 2,…,p, are incidence matrices of balanced incomplete block designs with the same number of treatments t, is a balanced block design with the block sizes exceeding the number of treatments. In derivation the matrix M₀, introduced by CALIński (1971) is utilized.