Rectangular designs

Combinatorial design theory is the study of families of subsets with various prescribed regularity properties. t designs, which are the most important structures of the design theory, are classified into the combinatorial designs. These designs play a vital role in reducing the structural expenses of the statistical experiments. Balanced incomplete block (BIB) designs are the special part of the t designs. Balanced incomplete block desings are t designs with t=2. Partially balanced incomplete block (PBIB) designs are special cases of BIB designs. Rectangular designs are 3-associate PBIB designs based on a rectangular association scheme of treatments arranged in an rectangle such that, with respect to each treatment, the first associates are the other n-1 treatments of the same row, the second associates are the other m-1 treatments of the same column and the remaining (m-1)(n-1) treatments are the third associates.