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The spectrum of additive BIB designs
Journal of Combinatorial Designs, 2007AbstractIn this article, the existence of additive BIB designs is discussed with direct and recursive constructions, together with investigation of a property of resolvability. Such designs can be used to construct infinite families of BIB designs.
M. Sawa +4 more
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Acta Mathematica Sinica, English Series, 2000
The author improves his estimate [J. Comb. Des. 4, No. 2, 83-93 (1996; Zbl 0913.05017)] of the upper bound for the smallest integer \(c(k,\lambda)\) such that \(v\in B(k,\lambda)\) for every integer \(v\geq c(k,\lambda)\) that satisfies the congruences \(\lambda v(v- 1)\equiv 0\;(\text{mod }k(k- 1))\) and \(\lambda(v- 1)\equiv 0\;(\text{mod }k- 1)\) in
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The author improves his estimate [J. Comb. Des. 4, No. 2, 83-93 (1996; Zbl 0913.05017)] of the upper bound for the smallest integer \(c(k,\lambda)\) such that \(v\in B(k,\lambda)\) for every integer \(v\geq c(k,\lambda)\) that satisfies the congruences \(\lambda v(v- 1)\equiv 0\;(\text{mod }k(k- 1))\) and \(\lambda(v- 1)\equiv 0\;(\text{mod }k- 1)\) in
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Results on the support of BIB designs
Journal of Statistical Planning and Inference, 1989This 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 ...
Hedayat, A. S. +2 more
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Journal of the Australian Mathematical Society, 1979
AbstractA series of balanced incomplete block (BIB) designs with parameters , is constructed, where , w any integer.
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AbstractA series of balanced incomplete block (BIB) designs with parameters , is constructed, where , w any integer.
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On a Family of Resolvable BIB Designs
Calcutta Statistical Association Bulletin, 1981In this paper we give a method of construction of a family of resolvable BIB designs with parameters v = p2 q, k = pq, λ = ( pq -1)⁄( q -1), where p is a prime or prime power and q is an integer such that p ⩾ q ⩾ 2 and ( pq- 1 )⁄( q -1) is an integer.
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BIB(9, 18t, 8t, 4, 3t) designs with repeated blocks
Journal of Statistical Planning and Inference, 1988The set of distinct blocks of a BIB(\(\nu\),b,r,k,\(\lambda)\) design is referred to as the support of a design. Via a computer program based on the methods of tradeoff and composition of designs, a table of 105 BIB designs based on \(\nu =9\), \(k=4\) with support sizes \(18\leq b^*\leq \left( \begin{matrix} 9\\ 4\end{matrix} \right)=126\) except for \
Khosrovshahi, G. B., Mahmoodian, E. S.
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Difference families, difference matrices, and bib-designs
Mathematical Notes of the Academy of Sciences of the USSR, 1985The author continues his work on difference families in additive Abelian groups of finite orders [For earlier works see Mat. Sb., Nov. Ser. 99(141), 366-379 (1976; Zbl 0405.05010), and Mat. Zametki 32, No.6, 869- 887 (1982; Zbl 0506.05011)]. The present paper contains many interesting construction theorems.
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A relation between BIB designs and chemical balance weighing designs
Statistics & Probability Letters, 1987The paper gives a certain new construction method for optimum chemical balance weighing designs. It utilizes a relation between the incidence matrices of a set of BIB designs and the design matrix of a chemical balance weighing design.
Ceranka, B., Katulska, K.
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A class of BIB designs with repeated blocks
Journal of Applied Statistics, 2001Balanced incomplete block design (BIBD) with repeated blocks is studied in detail. Methods of construction of BIB designs with repeated blocks are developed so as to distinguish the usual BIBD and BIBD with repeated blocks. One additional parameter, say d, is considered here, where d denotes the number of distinct blocks present in the BIB design with ...
D. K. Ghosh, S. B. Shrivastava
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A study of BIB designs through support matrices
Journal of Statistical Planning and Inference, 1985The algebraic approach for studying BIB designs with repeated blocks, introduced by \textit{W. Foody} and \textit{A. Hedayat} [Ann. Stat. 5, 932-945 (1977; Zbl 0368.62054)] is further developed. The concept of a support matrix is introduced, and the connection between full column rank support matrices and irreducible designs is explored.
Hedayat, A., Pesotan, H.
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