Results 171 to 180 of about 4,321 (196)
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On the existence of BIB designs with large λ
Journal of Statistical Planning and Inference, 2001Abstract In this article we prove the following theorem: Suppose that v and k are given, v⩾k+2 and λ 0 (v,k)=( v−2 k−2 ) 2 ·4 v−k−1 . If λ(v−1)≡0 ( mod k−1) , λv(v−1)≡0 ( mod k(k−1)) and λ>λ0(v,k), then there is a B(v,k,λ).
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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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Biometrical Journal, 1980
AbstractIn addition to the first part we prove independently of the model some theorems on properties of balanced block designs. Then we propose nine methods of construction of BIB and prove theorems in connection with these methods. In a table we give a survey on block designs with v$25 and possibilities of their construction with these methods ...
Rasch, D., Herrendörfer, G.
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AbstractIn addition to the first part we prove independently of the model some theorems on properties of balanced block designs. Then we propose nine methods of construction of BIB and prove theorems in connection with these methods. In a table we give a survey on block designs with v$25 and possibilities of their construction with these methods ...
Rasch, D., Herrendörfer, G.
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Combinatorics of Incidence Structures and Bib-Designs
1983We give an exposition of basic properties of incidence structures and designs (BIB-designs). Some properties relating internal and external structures, duality, and complementary structures are stated. We add some basic constructions for BIB-designs.
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A recursive method of construction of resolvable BIB-designs
Mathematical Notes of the Academy of Sciences of the USSR, 1977A theorem is proved that every resolvable BIB-design (v,k,λ) with λ=k−1 and the parameters v and k such that there exists a set of k−1 pairwise orthogonal Latin squares of order v can be embedded in a resolvable BIB-design ((k+1)v, k, k−1). An analogous theorem is established for the class of arbitrary BIB-designs.
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On the Construction of BIB Designs with Variable Support Sizes.
1980Abstract : A balanced incomplete block (BIB) design with b blocks is said to have support size b* when exactly b* of the b blocks are distinct. The importance and the applications of BIB designs with b* b in design of experiments and controlled sampling were explained in detail in Foody and Hedayat (1977) and Wynn (1977).
H. L. Hwang, A. Hedayat
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The Trade-Off Method in the Construction of BIB Designs with Variable Support Sizes
Annals of Statistics, 1979A Hedayat
exaly
A Note on the Block Structure of BIB Designs
Calcutta Statistical Association Bulletin, 1963openaire +2 more sources
The Construction of Pairwise Additive Minimal BIB Designs with Asymptotic Results
Applied Mathematics, 2014Kazuki Matsubara, Sanpei Kageyama
exaly