It has been shown in  that all partially balanced incomplete block (PBIB) designs with two associate classes, can be divided into a small number of types according to the nature of the association relations among the treatments. One simple and important type is the group divisible (GD). The combinatorial properties of GD designs have been studied in  and the analysis along with that for other types is given in . Here we give methods of constructing GD designs. These designs are likely to prove useful in agricultural, genetic and industrial experiments.
R. C. Bose. S. S. Shrikhande. K. N. Bhattacharya. "On the Construction of Group Divisible Incomplete Block Designs." Ann. Math. Statist. 24 (2) 167 - 195, June, 1953. https://doi.org/10.1214/aoms/1177729027