Balanced Designs with Unequal Numbers of Replicates

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.…”

Pairwise and variance balanced incomplete block designs

“…A block design is said to be an n-ary block design if the entries of N constitute n distinct integers (Das and Rao [9], Murty and Das [14], Rao and Das [16], and Tocher Note that all these generated designs will be equireplicated. This fact has led several authors (Adhikary [1], [2], Agrawal [3], Agrawal and Raghavachari [4], Calinski [7], Hedayat and Federer [12], and John [13]) to consider the construction of non-equireplicated pairwise balanced incomplete block designs.…”

“…Let o~ be a treatment not included in t2,. Utilizing the augmentation idea of Das [8], Federer [10], and John [13] we augment every block of D~ with oJ and call the resulting design /3~, i=l, 2,-.., it. Note that in general /9, is not variance balanced.…”