What is an infinite design?

Peter J. Cameron, Bridget S. Webb*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


It is usually assumed that an infinite design is a design with infinitely many points. This encompasses a myriad of structures, some nice and others not. In this paper we consider examples of structures that we would not like to call designs, and investigate additional conditions that exclude such anomalous structures. In particular, we expect a design to be regular, the complement of a design to be a design, and a t-design to be an s-design, for all 0 < s ≤ t. These are all properties that can be taken for granted with finite designs, and for infinite Steiner systems. We present a new definition of an infinite t-design, and give examples of structures that satisfy this definition. We note that infinite designs considered in the literature to date satisfy our definition. We show that infinite design theory does not always mirror finite design theory, for example there are examples of designs with v > b.

Original languageEnglish
Pages (from-to)79-91
Number of pages13
JournalJournal of Combinatorial Designs
Issue number2
Publication statusPublished - 1 Dec 2002


  • Infinite design


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