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Results on the support of BIB designs. (English) Zbl 0674.05006

This paper presents further results on BIB designs with repeated blocks by the first author in collaboration with two new co-authors. Let \(BIB(v,b,r,k,\lambda)/b^*)\) denote a BIB (v,b,r,k,\(\lambda)\) design with precisely \(b^*\) distinct blocks. The set of all distinct blocks is called the support of the BIB design and the number \(b^*\) is called the support size of the design. The authors present new lower bounds on \(b^*\) by using information about those blocks in the support which are repeated \(\lambda\) times in the design. They also provide the following specific results: (i) the nonexistence of \(BIB(8,56t,21t,3,6t| b^*)\) designs with \(b^*\leq 21\) (the design with support size 22 being already available; (ii) the non-existence of \(BIB(11,55t,15t,3,3t| b^*)\) designs with \(b^*\leq 24\) and the existence by actual construction of BIB(11,55,15,3,3\(| 25)\); (iii) the construction of BIB(12,44,11,3,2\(| 28)\) design, which has the minimum support size within the family of BIB(12,44t,11t,3,2t) designs.
Reviewer: B.L.Raktoe

MSC:

05B05 Combinatorial aspects of block designs
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References:

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