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Pairwise Balanced Designs with Block Sizes Three and Four

Published online by Cambridge University Press:  20 November 2018

Charles J. Colbourn ,
Alexander Rosa  and
Douglas R. Stinson
Charles J. Colbourn
Affiliation:
Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario N2L 3G1
Alexander Rosa
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario L8S 4K1
Douglas R. Stinson
Affiliation:
Department of Computer Science and Engineering, University of Nebraska - Lincoln, Lincoln, Nebraska 68858, U.S.A.
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Abstract

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Given integers ν, a and b, when does a pairwise balanced design on ν elements with a triples and b quadruples exist? Necessary conditions are developed, and shown to be sufficient for all v ≥ 96. An extensive set of constructions for pairwise balanced designs is used to obtain the result.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 4 , 01 August 1991 , pp. 673 - 704
Copyright
Copyright © Canadian Mathematical Society 1991

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