Some constructions of PBIB designs

Abstract

SummaryConstructions of three series of regular GD and semi-regular GD designs are given. Furthermore, a series of rectangular PBIB designs is constructed and particular cases of this series which reduce to PBIB designs with two associate classes are also provided.

On Certain Classes of Rectangular Designs

“…RI: [ (1,6,8,11,13,18); (2,4,9,12,14,16); (3,5,7,10,15,17)]; RII: [ (1,5,9,11,15,16); (2,6,7,12,13,17); (3,4,8,10,14,18)]; RIII: [(1, 6, 9, 10, 14, 17); (2,4,7,11,15,18); (3,5,8,12,13,16)];…”

“…Vartak [52] , Raghavarao and Aggarwal [37] , Kageyama and Tanaka [22] , Banerjee et al, [4] Bhagwandas et al, [6] Suen [51] , Sinha [45] , Kageyama and Miao [23] , Sinha and Mitra [48] , Sinha et al [46,47,49] , Kageyama and Sinha [24] , Bagchi [2,3] have constructed RDs using various approaches. Their construction methods may be summarized as:…”

“…Raghavaro and Aggarwal [37] From difference sets Kageyama and Tanaka [22] From BIBDs (v, k, λ) and Skew Hadamard designs Bhagwandas et al [6] From BIBDs (v, k, λ) Banerjee et al [4] From Rectangular association scheme Banerjee and Kageyama [5] From association scheme of GDD Puri et al (1987) [54] From partially efficiency-balanced (PEB) designs…”

“…We observe that the most general class of BIBDs satisfying the conditions of the Theorem [viz. 4 [33] ). Hence the improved version of Theorem 2.7 of Saurabh and Sinha [42] is:…”

Composite construction of group divisible designs

“…Clatworthy (1973) tabulated 443 parameters' combinations of GD designs with their solutions. Since then Freeman (1976), Kageyama and Tanaka (1981), Bhagwandas and Parihar (1982), Kageyama (1985aKageyama ( , 1985b, Mohan (1985a, 1985b), Banerjee et al (1985aBanerjee et al ( , 1985b, Bhagwandas et al (1985), Dey and Nigam (1985), Banerjee and Kageyama (1986), Sinha and Kageyama (1986), and Sinha (1987) have given several methods of constructing GD designs. From another point of view, Hanani (1975) also presented some methods of constructing GD designs.…”