MacNeish's conjecture was disproved by Parker (12) who showed that in certain cases N(v) > n(v) by proving that if there exists a balanced incomplete block (BIB) design with v treatments, A = 1, and block size k which is a prime power then N(v) > k — 2, and that this result can be improved to N(v) > k — 1, when the design is symmetric and cyclic. Parker's result though it did not disprove Euler...

Techniques and results of constructing balanced incomplete block designs from a Frobenius group were summarized in [2]. These techniques and results grew out of observing that the sets Na + b of a planar near-ring (N, +, .) usually have a geometric interpretation. This observation was first illustrated in [1]. In this same work, one notices that sometimes the sets N{a,-a} + b also have geometri...

Methods developed for the recursive construction of sets of balanced incomplete block designs with adjusted orthogonality (OBIBDs) are applied to designs with block size 4, with 2 sets of treatments. The methods are extended to include designs with blocks of size 4 nested into sub-blocks of size 2. We also complete the existence results of Greig and Rees for OBIBDs with block size 3 and 2 sets ...

1. Introduction These designs were introduced by Yates in order to eliminate heterogeneity to a greater extent than is possible with randomized blocks and Latin squares when the number of treatments is large. The precision of the estimate of a treatment effect depends on the number of replications of the treatment-the larger the number of replications, the more is the precision. Similar is the ...

Assaf, A.M., A. Hartman and N. Shalaby, Packing designs with block size 6 and index 5, Discrete Mathematics 103 (1992) 121-128. A (v, K, A) packing design of order v, block size K and index 1 is a collection of K-element subsets, called blocks, of a v-set V such that every 2-subset of V occurs in at most I blocks. The packing problem is to determine the maximum number of blocks in a packing des...

In this paper, we constructed (2, 7)-anonymous threshold scheme from the (49, 56, 8, 7, 1) Resolvable Balanced Incomplete Block Design (RBIBD) using MATLAB codes. The (2, 7)-anonymous threshold scheme was then applied to Result Processing Scheme in the Department of Statistics, University of Ibadan. The scheme developed satisfied the security requirements of authenticity, integrity and verifiab...

Using Lagrange’s multiplier rule, we find upper and lower bounds of the energy of a bipartite graph G, in terms of the number of vertices, edges and the spectral moment of fourth order. Moreover, the upper bound is attained in a graph G if and only if G is the graph of a symmetric balanced incomplete block design (BIBD). Also, we determine the graphs for which the lower bound is sharp.  2003 E...