The minimum number of blocks in pairwise balanced designs with maximum block size 4: the final cases

M Gruettmueller, Ian Roberts, S D'arcy, J Egan

    Research output: Contribution to journalArticle

    Abstract

    The minimum number of blocks having maximum size precisely four that are required to cover, exactly ? times, all pairs of elements from a set of cardinality v is denoted by g? (4)(v) (or g(4)(v) when ? = 1). All values of g? (4) (v) are known except for ? = 1 and v = 17 or 18. It is known that 30)? g(4)(l7) ? 31 and 32 ? g(4)(l8) ? 33. In this paper we show that g(4)(17?30 and g(4)(18) ? 32, thus finalising the determination of g? (4)v) for all ? and v.
    Original languageEnglish
    Pages (from-to)303-313
    Number of pages11
    JournalAustralasian Journal of Combinatorics
    Volume36
    Publication statusPublished - 2006

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