Construction of Rectangular Designs

Block Designs: A Randomization Approach

“…Then nI = t -1, n2 = s -1, n3 = (s -1) ( 'l/Jl = r-Al +(8-1)(A2-A3), ' l/J2 = r-A2+(t-1)(Al-A3), 'l/J3 = r-Al-A2+ A3, PI = t -1, P2 = 8 -1, P3 = (8 -1)(t -1), Example 6.0.6. Based on the 3 x 2 rectangular scheme of six treatments, the following incidence matrix right gives a rectangular design, No.4 in Table 1 of Sinha, Kageyama and Singh (1993), with parameters v = 6, b = 8, r = 4, k = 3, Al = 0, A2 = 3, A3 = 1,8 = 3, t = 2: (F) A group divisible 3-associate association scheme (a special case of Raghavarao, 1971, Section 8.12.6). There are v = 818283 treatments each denoted by three indices (iI, i2, i3), i l = 1,2, ... ,81; i2 = 1,2, ... ,82; i3 = 1,2, ... ,83.…”

“…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).…”

Constructions of Resolvable Group Divisible Designs and Related Designs

“…A nested BIB design, (16, 25, 34) mod 7, with parameters v = 7 = b 1 , r = 6 = k 1 , λ 1 = 5, b 2 = 21, k 2 = 2, λ 2 = 1 (Preece [8]), yields an RGD design with parameters v * = 24 = b * , r * = 7 = k * , λ * 1 = 0, λ * 2 = 2, m * = 8, n * = 3, which is a frame, whose solution is obtained by developing (α, 1, 6,9,12,17,18), (β, 3,4,8,13,16,19), (γ, 2, 5, 10,11,15,20) in partial cycles of (1 to 7, 8 to 14, 15 to 24), and α, β, γ being invariant, along with three more blocks, (1, 2, 3, 4, 5, 6, 7), (8,9,10,11,12,13,14), (15,16,17,18,19,20,21).…”

“…Recent constructions on rectangular designs may be found in Sinha et al [15][16][17][18]. By adding the two blocks formed as (i) (1, 2, .…”

“…Good sources of references, for GD designs are Clatworthy [1], Raghavarao [9], Sinha [11], for nested GD designs are Miao et al [5], Mitra et al [6], for rectangular designs are Sinha et al [15][16][17][18].…”