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Existence of resolvable group divisible designs with block size four I

Discrete Mathematics, 2002
It is proved in this paper that for m≢0,2,6,10(mod12) there exists a resolvable group divisible design of order v, block size 4 and group size m if and only v≡0(mod4), v≡0(modm), v−m≡0(mod3), except when (m,v)=(3,12) and except possibly when (3,264),(3 ...
Shen, Hao, Shen, Jiaying, Jiaying Shen, Hao Shen   +3 more
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Group-divisible rotatable designs

Annals of the Institute of Statistical Mathematics, 1967
By modifying the restrictions imposed on the levels of the factors in a second order rotatable design, an alternative series of response surface designs has been obtained. Thev factors of the design have been split into two groups, and the design is rotatable for each group of factors when the levels of the factors in the other group are held constant.
Das, M. N., Dey, A.
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Constructions of Resolvable Group Divisible Designs and Related Designs

Annals of Combinatorics, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mitra, R. K., Sinha, K., Mandal, N. K., Kageyama, S.   +3 more
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The Asymptotic Existence of Resolvable Group Divisible Designs

Journal of Combinatorial Designs, 2012
AbstractA group divisible design (GDD) is a triple which satisfies the following properties: (1) is a partition of X into subsets called groups; (2) is a collection of subsets of X, called blocks, such that a group and a block contain at most one element in common; and (3) every pair of elements from distinct groups occurs in a constant number λ ...
Chan, Justin H., Dukes, Peter J., Lamken, Esther R., Ling, Alan C. H.   +3 more
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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 construction of group divisible designs

Journal of Statistical Planning and Inference, 1985
The author shows that ''the existence of a resolvable BIB design with parameters \((v=\beta k,b,r,k,\lambda)\) which is not affine, implies the existence of a resolvable regular GD design with parameters: \((v^*=\beta k\), \(b^*=b-\beta\), \(r^*=r-1\), \(k^*=k\), \(\lambda^*_ 1=\lambda -1\), \(\lambda^*_ 2=\lambda\), \(m^*=\beta\), \(n^*=k)''\).
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A construction of group divisible designs

Journal of Statistical Planning and Inference, 1979
Abstract Given any affine design with parameters v, b, r, k, λ and μ = k2/v and any design with parameters v′, b′, r′, k′, λ′ where r′ = tr for some natural number `t and k′⩽r, we construct a group divisible design with parameters v′' = vv′, m = v′, n = v, b′' = vb′, k′' = kk′, r′'= kr′, λ1 = tkλ and λ2 = μλ′.
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A Complete Generalization of Clatworthy Group Divisible Designs

SIAM Journal on Discrete Mathematics, 2011
Partially balanced incomplete block designs (PBIBDs) have a long history and have been extensively used in agriculture and industrial experiments. Since the book of Clatworthy on two-associate-class partially balanced designs was published in 1973, little progress has been made on the construction of these designs. Group divisible designs (GDDs) are an
Fei Gao, Gennian Ge
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A class of group divisible 3‐designs and their applications

Journal of Combinatorial Designs, 2008
AbstractIn this article, we first show that a group divisible 3‐design with block sizes from {4, 6}, index unity and group‐type 2m exists for every integer m≥ 4 with the exception of m = 5. Such group divisible 3‐designs play an important role in our subsequent complete solution to the existence problem for directed H‐designs DHλ(m, r, 4, 3)s.
Wang, Jian Min, Ji, Lijun
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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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