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Defining sets of full designs with block size three II

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Donovan, Diane
Lefevre, James
Waterhouse, Mary

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A defining set of a t-(v, k, lambda) design is a subcollection of its blocks which is contained in a unique t-design with the given parameters. A minimal defining set is a defining set, none of whose proper subcollections is a defining set. The spectrum of minimal defining sets of a design D is the set {|M| | M is a minimal defining set of D}. The unique simple design with parameters is said to be the full design on v elements. This paper studies the minimal defining sets of full designs when t = 2 and k = 3. The largest known minimal defining set is given. The existence of a continuous section of the spectrum comprising asymptotically 9v (2)/50 values is shown. This gives a quadratic length section of continuous spectrum where only a linear section with respect to v was known before.

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Springer

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Applied mathematics

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Annals of Combinatorics

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10.1007/s00026-012-0143-8

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