Equi-replicated balanced block designs generated by a balanced matrix

In this paper it is shown that if N= documentclass{article}pagestyle{empty}begin{document}$ mathop sum limits_{i = 1}^{S_h} $end{document} c_ihN_ih, where c_ih are some non-negative integer numbers and N_ih are such incidence matrices that A_h = documentclass{article}pagestyle{empty}begin{document}$ mathop sum limits_{i = 1}^{S_h} $end{document} i N_ih is a balanced matrix defined by SHAH (1959), for h = 1, 2,…, p, then a block design with an incidence matrix Ñ = [N, N,…,N] is an equi-replicated balanced block design. Here the balance of a block design is defined in terms of the matrix M₀ introduced by CALI?SKI (1971).