On complete classes of experiments for certain invariant problems of linear inference

For certain non-singularly estimable full-rank appropriately invariant problems of linear inference in the setting of block designs, some complete classes of experiments have been characterized through the relation between the relevant C-matrices and their g-inverses (of the Moore-Penrose type) in regard to the specific invariance criterion discussed here. It follows that for a $\text{G}$-invariant non-singularly estimable full-rank problem, a complete class of experiments formally consists only of $\text{G}$-invariant designs.