A pairwise balanced design is an ordered pair S,B , denoted PBD S,B , where S is a finite set of symbols, and B is a collection of subsets of S called blocks, such that each pair of distinct elements of S occurs together in exactly one block of B. Here |S| v is called the order of the PBD. Note that there is no condition on the size of the blocks in B. If all blocks are of the same size k, then...

Given a design V, other designs can be constructed by using unions of various sets of blocks as new blocks. This method of constructing designs is referred to as "the union method". In general, the constructed design has neither constant blocksize nor balance properties. Various situations in which balanced incomplete block designs (BIBD's) and group divisible designs (GDD's) can be constructed...

durbin's rank test is widely used for testing treatment effects in balanced incomplete block designs (bibds)which have wide applications in sensory analysis. this test is failed for bibds when ties data occur. an adjusted version of durbin rank test for this kind of data is given to solve this problem. chi-square approximation, which is commonly used for this test, is not adequate for small bib...

The Cochran–Mantel–Haenszel (CMH) tests apply when every treatment is present on block or stratum and responses are categorical. This chapter explains the most elementary of incomplete designs, balanced design (BIBD), in part to see how CMH methods can aid analysis for such designs. relationship shows that adjusted Durbin test ANOVA F essentially same test, so both equality mean ranks, not mere...

A balanced incomplete block design (BIBD) is instrumental in design of experiments. This is usually constructed by algebraic methods such as finite algebra or difference sets. However, in algebraic approaches, no unified method exists, and each BIBD has been constructed in some ad hoc ways. On the other hand, computer-based methods apply the same algorithm to all BIBDs; hence, these are unified...

BIBD (balanced incomplete block design) is instrumental in design of experiments. This is usually constructed using algebraic tools such as finite projective (or affine) algebra or difference sets. Recently, heuristic algorithms have been tried, including artificial neural networks, simulated annealing, and local search method. In this paper, we present a novel approach to construct BIBDs that ...

Large number of watermarks is crucial for some real watermarking applications, such as transaction tracking. The purpose of this paper is to enlarge the set of structured watermarks based on balanced incomplete block designs (BIBD). An approach is proposed to generate new structured watermarks by combining existing BIBD-based watermarks. The corresponding recognition rules for the new set of wa...

It has been shown that for k = 8 or 9, there exists a BIBD(v, k, 1) for all positive integers v == 1 or k (mod k(k-1)), with some possible exceptions. We show that such designs exist for 49 of these exceptional values. A balanced incomplete block design (BIBD) with parameters (v, k, 1) is a pair (X, A) where X is a v-set and A is a family of k-subsets (where 2 < k < v) called blocks, such that ...

For asynchronous Wireless Sensor Networks (WSNs), this research suggests an ideal Balanced Incomplete Block Design (BIBD) extended design based neighbour finding technique. The algorithm takes use of the characteristics BIBD designs to build a series transmission plans that guarantee effective detection with little energy consumption and delay. Simulations are used test proposed algorithm, resu...

A design D consists of a family B1 , ..., Bb of subets, called blocks, of a finite set S=[P1 , ..., Pv] whose elements are called points or varieties. D is balanced or *-linked if every pair of points is contained in exactly * blocks. If, in addition, *>0 and no block contains all the points, then D is nontrivial, and if every block has the same cardinality k then D is a balanced incomplete-blo...