Some rectangular designs constructed by the method of differences

Block Designs: A Randomization Approach

“…See, for example, Suen (1989), Gupta and Mukerjee (1989), Sinha (1991b), Sinha, Kageyama and Singh (1993), Kageyama and Miao (1995a), and Sinha, Singh, Kageyama and Singh (2002). Extensive lists of rectangular designs in the range of parameters 2 ~ r, k ~ 10 are given by Sinha, Kageyama and Singh (1993) and Sinha, Singh, Kageyama and Singh (2002).…”

Balanced arrays of strength two from block designs

“…A rectangular design is an arrangement of v ¼ mn treatments in b blocks such that (i) each block contains k distinct treatments, k < v, (ii) each treatment occurs in exactly r blocks, (iii) the mn treatments are arranged in a rectangle of m rows and n columns such that any two treatments in the same row (column) occur together in 1 ( 2 ) blocks, respectively, and in 3 blocks otherwise. Some constructions and references on rectangular designs may be found in [15,16,22]. These designs are here used to construct balanced arrays.…”

Some Patterned Constructions of Rectangular Designs

“…These designs have been studied by Bhagwandas and Kageyama (1985), Suen (1989), Sinha (1991), Sinha et al (1993Sinha et al ( , 1996Sinha et al ( , 1999, Kageyama and Miao (1995), Sinha et al (2002b), and so on. The rectangular designs are useful as factorial experiments, having balance as well as orthogonality (Gupta and Mukerjee, 1989).…”

“…The rectangular designs are useful as factorial experiments, having balance as well as orthogonality (Gupta and Mukerjee, 1989). In addition, if λ 3 is bigger than λ 1 and λ 2 , the loss of information on the main effects becomes small (Suen, 1989), when these designs are used as an m×n complete confounded factorial experiments. A review of constructional procedures for these designs is given by Gupta and Mukerjee (1989).…”

“…In this paper, some patterned constructions of rectangular designs are given along with a table of new designs in the range of r, k ≤ 10 and not found in the tables of Suen (1989), Sinha et al (1993Sinha et al ( , 1996, and Sinha et al (2002b).…”