Some Series of SGDD's with the Dual Property, BOD's and BIBD's

1981 ◽  
Vol 30 (3-4) ◽  
pp. 115-122
Author(s):  
A. C. Mukhopadhyay
Keyword(s):  
Prime Number ◽  
Infinite Series ◽  
Prime Power ◽  
Block Designs ◽  
Incomplete Block ◽  
Balanced Incomplete Block Designs ◽  
Dual Property ◽  
Group Divisible ◽  
Symmetrical Group ◽  
Balanced Incomplete Block

In the present paper an infinite series of Ba1am:ed ortbozonal designs (BOD's) is constructed for each s, an odd prime number or prime power and hence some infinite series of balanced incomplete block designs (BIBD's) and symmetrical group divisible designs (SGDD's) witb dual Ptoperty. Following Bose (1977), equivalences of some series of SGDD's with dual property are cstablished and their equivalence with corresponding series of BOD's is pointed out.

Generalized Hadamard Matrices and Orthogonal Arrays of Strength Two

1964 ◽  
Vol 16 ◽  
pp. 736-740 ◽  
Author(s):  
S. S. Shrikhande
Keyword(s):  
Block Design ◽  
Orthogonal Arrays ◽  
Hadamard Matrices ◽  
Block Designs ◽  
Incomplete Block ◽  
Balanced Incomplete Block Design ◽  
Balanced Incomplete Block Designs ◽  
Group Divisible ◽  
Incomplete Block Design ◽  
Balanced Incomplete Block

The purpose of this note is to point out some connexions between generalized Hadamard matrices (4, 5) and various tactical configurations such as group divisible designs (3), affine resolvable balanced incomplete block designs (1), and orthogonal arrays of strength two (2). Some constructions for these arrays are also indicated.A balanced incomplete block design (BIBD) with parameters v, b, r, k, λ is an arrangement of v symbols called treatments into b subsets called blocks of k < v distinct treatments such that each treatment occurs in r blocks and any pair of treatments occurs in λ blocks.

On a Method of Construction of Balanced Incomplete Block Designs

1986 ◽  
Vol 35 (3-4) ◽  
pp. 157-160
Author(s):  
D. V. S. Sastry ◽  
R. H. Malgaonkar
Keyword(s):  
Block Designs ◽  
Incomplete Block ◽  
Group Divisible Designs ◽  
Balanced Incomplete Block Designs ◽  
Group Divisible ◽  
Balanced Incomplete Block

This paper gives a method of construction of balanced incomplete block designs (BIBDs) and group divisible designs from the existing self complementary BIBDs.

Existence of simple BIBDs from a prime power difference family with minimum index

2019 ◽  
Vol 18 (09) ◽  
pp. 1950166
Author(s):  
Hsin-Min Sun
Keyword(s):  
Simple Formula ◽  
Prime Power ◽  
Block Designs ◽  
Incomplete Block ◽  
Difference Family ◽  
Balanced Incomplete Block Designs ◽  
Extensive Analysis ◽  
Power Difference ◽  
Balanced Incomplete Block ◽  
Minimum Index

We show that under certain technical conditions that simple [Formula: see text] balanced incomplete block designs (BIBDs) exist for all allowable values of [Formula: see text], where [Formula: see text] is an odd prime power. Our primary technique is to argue for the existence of difference families in finite fields, in the flavor of Wilson [J. Number Theory 4 (1972) 17–47]. We provide an extensive analysis in the cases, where [Formula: see text] and also for [Formula: see text].

scholarly journals Semiregular group divisible designs with dual properties

1992 ◽  
Vol 45 (1) ◽  
pp. 61-69
Author(s):  
Alan Rahilly
Keyword(s):  
Construction Method ◽  
Block Designs ◽  
Incomplete Block ◽  
Group Divisible Designs ◽  
Balanced Incomplete Block Designs ◽  
Group Divisible ◽  
Transversal Designs ◽  
Balanced Incomplete Block

A construction method for group divisible designs is employed to construct (i) infinitely many non-symmetric semiregular group divisible designs whose duals are semiregular group divisible designs, and (ii) infinitely many transversal designs whose duals are group divisible 3-associate designs. A construction method for affine α−resolvable balanced incomplete block designs is also given and illustrated.

scholarly journals A Construction Technique for Group Divisible (v-1,k,0,1) Partially Balanced Incomplete Block Designs (PBIBDs)

2021 ◽  
pp. 23-30
Author(s):  
Oluwaseun A. Otekunrin ◽  
Kehinde O. Alawode
Keyword(s):  
Block Designs ◽  
Incomplete Block ◽  
Combinatorial Structures ◽  
Construction Technique ◽  
Balanced Incomplete Block Designs ◽  
Group Divisible ◽  
Balanced Incomplete Block ◽  
Block Cutting

Group Divisible PBIBDs are important combinatorial structures with diverse applications. In this paper, we provided a construction technique for Group Divisible (v-1,k,0,1) PBIBDs. This was achieved by using techniques described in literature to construct Nim addition tables of order 2n, 2≤n≤5 and (k2,b,r,k,1)Resolvable BIBDs respectively. A “block cutting” procedure was thereafter used to generate corresponding Group Divisible (v-1,k,0,1) PBIBDs from the (k2,b,r,k,1)Resolvable BIBDs. These procedures were streamlined and implemented in MATLAB. The generated designs are regular with parameters(15,15,4,4,5,3,0,1);(63,63,8,8,9,7,0,1);(255,255,16,16,17,15,0,1) and (1023,1023,32,32,33,31,0,1). The MATLAB codes written are useful for generating the blocks of the designs which can be easily adapted and utilized in other relevant studies.   Also, we have been able to establish a link between the game of Nim and Group Divisible (v-1,k,0,1) PBIBDs.

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