Some Patterned Constructions of Rectangular Designs

Kageyama, Sanpei; Sinha, Kishore

doi:10.14490/jjss.33.137

Cited by 6 publications

(9 citation statements)

References 11 publications

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“…Vartak [52] , Raghavarao and Aggarwal [37] , Kageyama and Tanaka [22] , Banerjee et al, [4] Bhagwandas et al, [6] Suen [51] , Sinha [45] , Kageyama and Miao [23] , Sinha and Mitra [48] , Sinha et al [46,47,49] , Kageyama and Sinha [24] , Bagchi [2,3] have constructed RDs using various approaches. Their construction methods may be summarized as:…”

Section: Earlier Constructionsmentioning

confidence: 99%

On Certain Classes of Rectangular Designs

Singh

Saurabh

2023

Calcutta Statistical Association Bulletin

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Rectangular designs are classified as regular, Latin regular, semi-regular, Latin semi-regular and singular designs. Some series of self-dual as well as α–resolvable designs which belong to the above classes are obtained. The building blocks of the designs are square (0, 1)-matrices. It is more general to view a class of designs based on an array than to view them based on disjoint groups of treatments of equal size. This generality enabled us to identify three subclasses of rectangular designs: Latin regular RDs, Latin semi-regular RDs and semi-regular L2-type designs which deserve further study. In every construction we obtain a matrix N with square (0, 1)-submatrices such that N becomes the incidence matrix of a rectangular design. The method is the reverse of the well-known tactical decomposition of the incidence matrix of a known design. The authors have already obtained some series of Group Divisible and L2-type designs using this method. Tactical decomposable designs are of great interest because of their connections with automorphisms of designs, see Bekar et al.[ 1 ] The rectangular designs constructed here are of statistical as well as combinatorial interest. AMS Subject Classification: 62K10; 05B05

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Section: Earlier Constructionsmentioning

confidence: 99%

On Certain Classes of Rectangular Designs

Singh

Saurabh

2023

Calcutta Statistical Association Bulletin

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“…The above set of n 2 blocks constitutes a PBIB design with the generalized parameters as given below: (15,11,12,13,14,20,25,5,10,16,22,3,9) B16: (16,17,18,19,20,21,1,6,11,22,3,9,15) B17: (17,18,19,20,16,22,2,7,12,23,4,10,11) B18: (18,19,20,16,17,23,3,8,13,24,5,6,12) B19: (...…”

Section: Constructionmentioning

confidence: 99%

“…Let us illustrate the above construction methodology for n = 6. Now using the matrix S(1) and following the above construction methodology, we will obtain the following set of 12 blocks: B1: (1, 2, 3, 4, 5, 6) B7: (2, 8, 14, 20, 26, 32) B2: (19,20,21,22,23,24) B8: (5,11,17,23,29,35) B3: (1,7,13,19,25,31) B9: (13,14,15,16,17,18) B4: (4,10,16,22,28,34) B10: (31, 32, 33, 34, 35, 36) B5: (7,8,9,10,11,12) B11: (3, 9, 15, 21, 27, 33) B6: (25,26,27,28,29,30) B12: (6, 12, 18, 24, 30, 36) The above set of blocks constitutes a three-associate class PBIB design with the following parameters:…”

Section: Constructionmentioning

confidence: 99%

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Construction of three-associate class PBIB designs by generating a set of square matrices

Sharma¹,

Garg

2022

J. Phys.: Conf. Ser.

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The present paper deals with the construction of three-associate class PBIB designs. For this, we have first discussed a procedure to generate a set of square matrices. The construction of this set of matrices has been completely generalized. Then using this set of matrices, we have proposed a new three-associate class association scheme based on which we have constructed some series of PBIB designs. The complementary designs of the proposed PBIB designs have also been discussed. At the end of the paper, a table has been given which enlists some of the PBIB designs constructed in this paper.

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“…They were introduced for the first time by (Vartak, 1955), since then, several construction methods have been proposed by (Singh et al, 2011;Kageyama and Sinha, 2003) using essentially the incidence matrices.…”

Section: Introductionmentioning

confidence: 99%

New Construction Method of Rectangular Partially Balanced Incomplete Block Designs and Singular Group Divisible Designs

Imane¹

2014

Journal of Mathematics and Statistics

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In this study, we propose a new method of construction of rectangular Partially Balanced Incomplete Block (PBIB) designs of size k = 2s and 2 ≤ s < l and singular Group Divisible (GD) designs of size k = 2l, l is the number of columns in a rectangular matrix containing v = n × l treatments. We give the parameters expression of the obtained designs. Furthermore, we provide two algorithms of calculation for practical use.

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Some Patterned Constructions of Rectangular Designs

Abstract: This paper describes some new patterned methods of constructing rectangular designs from balanced incomplete block (BIB) designs and nested BIB designs, and gives a table of rectangular designs in the range of r, k ≤ 10.

Cited by 6 publications

References 11 publications

On Certain Classes of Rectangular Designs

On Certain Classes of Rectangular Designs

Construction of three-associate class PBIB designs by generating a set of square matrices

New Construction Method of Rectangular Partially Balanced Incomplete Block Designs and Singular Group Divisible Designs

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