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S ummary This paper considers block designs and row-column designs where the information matrix  C  has two different nonzero eigenvalues, one of multiplicity 1 and the other of multiplicity  h −1, where  h  is the rank of the matrix  C . It was found that for each such design there exists a diagonal positive definite matrix  X  such that the design is  X −1 -balanced.

X−1-balance of some partially balanced experimental designs with particular emphasis on block and row-column designs

X⁻¹-balance of some partially balanced experimental designs with particular emphasis on block and row-column designs