Construction of Some Balanced Incomplete Block Designs with Nested Rows and Columns

Abstract

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Development of Research in Experimental Design in India

“…BIB designs with nested rows and columns form an important subclass of these designs. Such balanced designs were studied among others, by Singh & Dey (1979), Agrawal & Prasad (1982, 1983), Sreenath (1989, 1991) and Mukerjee & Gupta (1991). The issue of optimality of block designs with nested rows and columns was addressed by Bagchi et al (1990).…”

Some constructions for balanced incomplete block designs with nested rows and columns

“…Example 1: In geometry EG (2, 2 2 ), there are 16 points and 20 lines, the correspondence between points and treatments are given below: 1 9 1 13 1 5 5 13 9 5 13 9 3 10 3 16 3 5 5 16 10 5 16 10 2 10 2 14 2 6 6 14 10 6 14 10 4 9 4 15 4 6 6 15 9 6 15 9 3 11 3 15 3 7 7 15 11 7 15 11 1 11 1 15 1 8 8 15 11 (2,11,22,26,33,47,53,60); (3,10,20,27,39,41,56,62); (4,14,19,28,37,48,49,58); (5,16,23,29,36,46,50,57); (6,12,18,30,40,45,55,59); (7,9,12,31,35,42,54,<...>…”

“…In this paper some simple methods of construction of BIB-RC design are given. These methods are particular cases of the theorem 4.2.1. of Sreenath (1999), which states that the existence of a BIB design with parameters v, b, r, k, and a BIB-RC design with parameters k, b * , r * , u, w, * implies the existence of BIB-RC design with parameters v, bb * , rr * , u, w, * . In these designs blocks of BIB-RC design with parameters k, b * , r * , u, w, * are superimposed on the blocks of BIB design with parameter v, b, r, k, to form a BIB-RC design with parameters v, bb * , rr * , u, w, * .…”

On recursive construction for balanced incomplete block designs with nested rows and columns

“…Several methods of constructions of BIBRC s have been given by Singh & Dey (1979), Street (1981), Agrawal & Prasad (1982, 1983, Cheng (1986), Sreenath (1989), Uddin & Morgan (1990, 1991, Uddin (1992). Some designs for small v, p and q are listed by Preece (1967) and Ipinyomi & John (1985).…”