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Some \(V(12,t)\) vectors and designs from difference and quasi-difference matrices. (English) Zbl 1204.05026

Summary: In this paper, we provide examples of \(V(12,t)\) vectors for \(800 \leq 12t+1 \leq 5000\), and the \(3\) unknown \(V(m,t)\) vectors with \(m=8,9\). We also provide other examples of transversal designs and incomplete designs, coming from difference matrices and quasi-difference matrices. These include a \(\text{TD}(6,34)\), a \(\text{TD}(7,v)\) for \(v=28, 42, 44, 52, 54, 62\), an updated list of unknown \(\text{TD}_{\lambda}(9,v)\) for \(\lambda>1\) and 2 ITDs which give \((v,6,1)\) BIBDs for \(v \in \{496,526\}\).

MSC:

05B05 Combinatorial aspects of block designs
05B10 Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.)
05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.)
15B36 Matrices of integers
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