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On the minimum number of blocks defining a design

Published online by Cambridge University Press:  17 April 2009

Ken Gray
Ken Gray
Affiliation:
Department of Mathematics, University of Queensland, St Lucia Qld 4067, Australia
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Abstract

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A set of blocks which is a subset of a unique t – (v, k, λt) design is said to be a defining set of that design. We examine the properties of such a set, and show that its automorphism group is related to that of the whole design. Smallest defining sets are found for 2-designs and 3-designs on seven or eight varieties with block size three or four, revealing interesting combinatorial structures.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 41 , Issue 1 , February 1990 , pp. 97 - 112
Copyright
Copyright © Australian Mathematical Society 1990

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