Results 271 to 280 of about 17,937 (310)

A Note on Balanced Incomplete Block Designs

Canadian Journal of Mathematics, 1954
A balanced incomplete block design is defined as an arrangement of v objects in b blocks, each block containing k objects all different, so that there are r blocks containing a given object and λ blocks containing any two given objects. Such designs have been studied for their combinatorial interest, as in (3), and also for their application to ...
D. A. Sprott
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On Covering of Balanced Incomplete Block Designs

Canadian Journal of Mathematics, 1964
Given a set E of v elements and given positive integers k (k ≤ v) and λ, we understand by balanced incomplete block design (BIBD) B [k, λ, v] a system of blocks (subsets of E) having k elements each such that every pair of elements of E is contained in exactly λ blocks.A necessary condition for the existence of a design B [k, λ, v] is known to be (4)
Haim Hanani
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An Embedding Theorem for Balanced Incomplete Block Designs

Canadian Journal of Mathematics, 1954
From a symmetric balanced incomplete block design we may construct a derived design by deleting a block and its varieties. But a design with the parameters of a derived design may not be embeddable in a symmetric design. Bhattacharya (1) has such an example with λ = 3 .
Hall, Marshall jun., Connor, W. S.
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Balanced Incomplete Block Designs

, 2022
Block designs are useful in experimental design when the experimental material is not uniform but can be divided into homogeneous blocks. Typically, blocks cannot contain all the treatments, so incomplete block designs are used. The condition of balance,
Cameron, Peter J.
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Nearly Balanced Incomplete Block Designs

Biometrika, 1981
Abstract : A class of nearly balanced incomplete block designs is defined. This extends the concept of regular graph designs of John and Mitchell (1977) to the unequally replicated case. Some necessary conditions on the existence of such designs are derived. Methods of construction are given for some special cases. For five or six varieties, the 'best'
Cheng, Ching-Shui, Wu, Chien-Fu
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Balanced Incomplete Block Designs with Block Size 7

Designs, Codes and Cryptography, 1998
This paper makes considerable progress in fully determining the spectrum of balanced incomplete block designs (BIBDs) with block size \(k = 7\). This work was begun by \textit{H. Hanani} [Balanced incomplete block designs and related designs, Discrete Math. 11, 255-369 (1975; Zbl 0361.62067)] and continued by \textit{A. E. Brouwer, A.
R. Julian R. Abel, Malcolm Greig
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Balanced Incomplete Block Designs

Journal of the Institute of Actuaries, 1970
In my earlier paper I expressed disappointment at failure to find b.i.b.d.s for the case ν= 4p, k = 4, b = ½ν(ν−1), λ = 6 (p is an odd prime). The failure was not complete because I had given a solution for ν = p + 1, k = 4, λ = 6 which covered the cases of ν = 4p where ν−1 was also a prime.
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Construction of Nested Balanced Incomplete Block Designs

Calcutta Statistical Association Bulletin, 1986
A set of general methods for constructing Nested Balanced Incomplete Block Designs is presented. These methods lead to the solution of some new designs.
Dey, A., Das, U. S., Banerjee, A. K.
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Splitting balanced incomplete block designs [PDF]

Australas. J Comb., 2005
A \((v, 2k,\lambda)\)-splitting balanced incomplete block design is a BIBD where every block is the disjoint union of 2 subblocks of size \(k\) and for each 2-subset of points there exist \(\lambda\) blocks such that the points are in separate subblocks.
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