Equi‐replicated balanced block designs generated by a balanced matrix

In this paper it is shown that if N   * h = \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \sum \limits_{i = 1}^{S_h} $\end{document} c ih N ih , where c ih are some non‐negative integer numbers and N ih are such incidence matrices that A h = \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \sum \limits_{i = 1}^{S_h} $\end{document} i N ih is a balanced matrix defined by S HAH (1959), for h = 1, 2,…, p , then a block design with an incidence matrix Ñ = [ N   * 1 , N   * 2 ,…, N   * p ] is an equi‐replicated balanced block design. Here the balance of a block design is defined in terms of the matrix M 0 introduced by C ALIŃSKI (1971).