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Topics in balanced incomplete block designs

, 1973
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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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Equitably Colored Balanced Incomplete Block Designs

Journal of Combinatorial Designs, 2015
AbstractIn this paper, we determine the necessary and sufficient conditions for the existence of an equitably ℓ‐colorable balanced incomplete block design for any positive integer. In particular, we present a method for constructing nontrivial equitably ℓ‐colorable BIBDs and prove that these examples are the only nontrivial examples that exist. We also
Luther, Robert D., Pike, David A.
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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.
Abel, R. Julian R., Greig, Malcolm
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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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N-way balanced incomplete block designs

Journal of Statistical Planning and Inference, 1998
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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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Resolvable Balanced Incomplete Block Designs with Block Size 8

Designs, Codes and Cryptography, 1997
A balanced incomplete block design (BIBD) \(D\) is a collection \(B\) of subsets (blocks) taken from a finite set \(V\) of \(v\) elements with the properties: (1) every pair of distinct elements of \(V\) is contained in precisely \(\lambda\) blocks of \(B\), and (2) every block contains exactly \(k\) elements.
Greig, Malcolm, Abel, Julian
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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)
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