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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combinatorics
mathematics
block permutation group theory

computer science
combinatorial aspects of block designs
arithmetic

statistics
block design
discrete mathematics