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...

Wireless sensor networks are composed of very small devices, called sensor nodes,for numerous applications in the environment. In adversarial environments, the securitybecomes a crucial issue in wireless sensor networks (WSNs). There are various securityservices in WSNs such as key management, authentication, and pairwise keyestablishment. Due to some limitations on sensor nodes, the previous k...

A Sarvate–Beam Triple System SB(v, 3) is a set V of v elements and a collection of 3–subsets of V such that each distinct pair of elements in V occurs in i blocks, for every i in the list 1, 2, . . . , ( v 2 ) . In this paper, we completely enumerate all Sarvate-Beam Triple Systems for v = 5 and v = 6. (In the case v = 5, we extend a previous result of R. Stanton [8].) 1 Sarvate–Beam Designs Th...