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On Covering of Balanced Incomplete Block Designs
Canadian Journal of Mathematics, 1964Given 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)
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Nearly Balanced Incomplete Block Designs
Biometrika, 1981Abstract : 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 [PDF]
, 2010 https://rdc.reed.edu/v1/resources/9e768538-c7e7-4135-9967-bb9922a8cfc3/thumb/128.jpgIn this thesis, I develop the study of balanced incomplete block designs (BIBD's), which have interesting applications to statistical experiments and other fields of ...
Peterman, Mary
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Balanced Incomplete Block Designs with Block Size 7
Designs, Codes and Cryptography, 1998This 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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Nested balanced incomplete block designs of harmonised series [PDF]
Journal of the Nigerian Mathematical Society, 2015 Block designs are useful in comparative experimentation for improving efficiency of treatment comparisons when working with heterogeneous experimental units.
Saka, A.J., Adeleke, B.L.
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Nested balanced incomplete block designs derivable from simplex codes [PDF]
Journal of Discrete Mathematical Sciences and Cryptography, 2003 Preece (1967) introduced nested balanced incomplete block (NBIB) designs, which have two systems of blocks, second system nested within the first system. Systematic methods of construction of these designs have been discussed by various researchers.
M L Aggarwal
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Balanced Incomplete Block Designs
Journal of the Institute of Actuaries, 1970In 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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Partially Balanced Incomplete Block Design
2006This article provides a brief overview of the most common partially balanced incomplete block designs and discusses other designs to which they are related.
Street, D. J., Street, A. P.
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‘A New Solution of a Balanced Incomplete Block Design’
Calcutta Statistical Association Bulletin, 1987Solution of a new balanced incomplete block design for v=22, b=44, r=l4, k=7 and λ=4 is given. The design is obtained using the method of symmetrically repeated differences.
Manjit Singh, Jagroop Kaur
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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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