r-GRCdesigns

When the number of treatments is large with limited experimental resources then Row-Column(RC) designs with multiple units per cell can be used. These designs are called Generalized Row-Column (GRC) designs and are defined as designs with v treatments in p rows and q columns such that the intersection of each row and column (cell) consists of k experimental units. For example (Bailey & Monod (2001)<doi:10.1111/1467-9469.00235>), to conduct an experiment for comparing 4 treatments using 4 plants with leaves at 2 different heights row-column design with two units per cell can be used. A GRC design is said to be structurally complete if corresponding to the intersection of each row and column, there appears at least two treatments. A GRC design is said to be structurally incomplete if corresponding to the intersection of any row and column, there is at least one cell which does not contain any treatment.