Results 221 to 230 of about 36,439 (252)

Group divisible designs in MOLS of order ten

Designs, Codes and Cryptography, 2012
A famous open problem is to determine \(N(10)\), the cardinality of the largest set of mutually orthogonal Latin squares of order 10. It is known that \(2\leq N(10)\leq 6\). This paper proposes an interesting approach to trying to show that \(N(10)
Peter Dukes, Lea Howard
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A series of group divisible designs

Communications in Statistics - Theory and Methods, 1991
Bose and Shrikhande C19763 proved that if D(m, k, ⋋) is a Baer subdesign of another SBIBD D1 (v1, k1 ⋋), k1>k, then it also contains a complementary subdesign D* which is symmetric GDD, D* (v*, k*; ⋋-1, ⋋; m, n). Utilising this, we give a necessary condition for a SBIBD D to be a Baer subdesign of D1 and also give the parameters.
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A method of construction of regular group divisible designs

Biometrika, 1987
A method of construction of regular group divisible designs is described, which leads to two new designs.
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D‐optimal designs and group divisible designs

Journal of Combinatorial Designs, 2006
AbstractWe obtain new conditions on the existence of a square matrix whose Gram matrix has a block structure with certain properties, including D‐optimal designs of order $n\equiv 3 \pmod 4$, and investigate relations to group divisible designs. We also find a matrix with large determinant for n = 39. © 2006 Wiley Periodicals, Inc. J Combin Designs 14:
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Matrix constructions of family (A) group divisible designs [PDF]

Australas. J Comb., 2020
A new construction of (not necessarily symmetric) group divisible designs (GDD) with \(b= 4(r- \lambda_2)\) is described (\(b\) denotes the number of blocks of the design, and \(\lambda_2\) the number of blocks through two points in different point classes; \(r\) is the number of blocks through a point). GDDs with this property are called ``family (A)''
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Group divisible designs with large block sizes

Designs, Codes and Cryptography, 2017
In this paper, the author showed that there is a \((k,\lambda_k)\)-GDD, group divisible design, of type \((q^{l+1}-q^l)^{(q^{n-l}-1)/(q-1)}\), for any prime power \(q\) and any integers \(k\), \(n\) with \(3\leq k \leq n\), where \(\lambda_k=\frac{\prod_{i=3}^{k-1}(q^n-q^{l+i-1})}{(k-2)!}\) and \(k+l\leq n+1\).
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On Group Divisible Rotatable Designs

Calcutta Statistical Association Bulletin, 1976
Adhikary, Basudeb, Sinha, Bikas Kumar
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New Constructions of Divisible Design Cayley Graphs

Graphs and Combinatorics, 2021
Dean Crnkovic, Andrea Svob
exaly  

Classification of divisible design graphs with at most 39 vertices

Journal of Combinatorial Designs, 2022
Dmitry Panasenko, Leonid Shalaginov
exaly  

New versions of the Wallis-Fon-Der-Flaass construction to create divisible design graphs

Discrete Mathematics, 2022
V V Kabanov
exaly