Balanced Designs with Unequal Replications and Unequal Block Sizes

Block Designs: A Randomization Approach

“…The construction of such designs may be necessary when a BIB design with the corresponding v and b is not available, or when the blocks are naturally not of equal size (see Example 3.1.2). There are several methods of constructing such VB designs, for example, see Agrawal (1963), John (1964), Murty and Das (1967), Das and Rao (1968), Dey (1970), Kulshreshtha, Dey and Saha (1972), Hedayat and Federer (1974), Kageyama (1976dKageyama ( , 1988aKageyama ( , 1988b, Khatri (1982), Gupta and Jones (1983), Kumar (1984, 1986a), Mukerjee and Kageyama (1985), Jones, Sinha and Kageyama (1987), Pal and Pal (1988), Sinha (1988Sinha ( , 1989Sinha ( , 1990, Sinha and Jones (1988), Calvin and Sinha (1989), Hedayat and Stufken (1989), Gupta and Kageyama (1992), Ghosh, Joshi and Kageyama (1993), andKageyama (1996, 1997). Most of these methods utilize BIB designs and GD designs in their constructions.…”

“…It appears that the values of m and p above may get large as the number of treatments and/or block sizes increase, and thus these designs might not find much use in agricultural field experiments. However, they may be of use in some laboratory or industrial research (see the discussion in Tocher, 1952;Kulshreshtha, Dey and Saha, 1972;Puri and Nigam, 1977b). If N2 = Iv1" -N is taken with m = p = 1 for ko = c, the resulting pattern yields the incidence matrix of designs resulting from Theorems 6.6.7 -6.6.10, and Corollaries 10.…”

Characterization of equireplicated variance-balanced block designs

“…John [8] and Kulshreshtha, Dey and Saha [13] gave some methods for construction of n-ary BB designs. We here present other simple methods of constructing n-ary BB designs by modifying some methods given in [9] and [10].…”

“…Furthermore, it is known (cf. [6], [8], [9], [10], [11], [13], [16]) that an n-ary BB design with parameters v, b, v~, k s (i=1,2,...,v; j=1,2, 9 .., b) can be given by an incidence matrix N satisfying For an n-ary BB design, p also depends on an incidence structure of the design. The literature of block designs contains many articles exclusively related to BB designs.…”

“…The literature of block designs contains many articles exclusively related to BB designs. The interested reader can refer, for example, to [6], [8], [9], [10], [11], [13], [16] for details. In this paper, some block structure of equireplicated n-ary BB designs is investigated with illustrations.…”