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- W2000932883 abstract "A defining set of a t−(v, k, λ) 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 $${{t-left(v, k, begin{array}{ll}left(begin{array}{ll}v-t k-tend{array}right)end{array}right)}}$$ 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." @default.
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- W2000932883 date "2012-05-19" @default.
- W2000932883 modified "2023-10-07" @default.
- W2000932883 title "Defining Sets of Full Designs with Block Size Three II" @default.
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- W2000932883 doi "https://doi.org/10.1007/s00026-012-0143-8" @default.
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