scholarly journals Finite Euclidean Geometry Approach for Constructing Balanced Incomplete Block Design (BIBD)

2021 ◽  
pp. 47-59
Author(s):  
U. P. Akra ◽  
S. S. Akpan ◽  
T. A. Ugbe ◽  
O. E. Ntekim
Keyword(s):  
Euclidean Geometry ◽  
Dimensional Space ◽  
Block Design ◽  
Combinatorial Design ◽  
Incomplete Block ◽  
Balanced Incomplete Block Design ◽  
Estimation Of Parameters ◽  
Design Structure ◽  
Incomplete Block Design ◽  
Balanced Incomplete Block

In block design, construction of Balanced Incomplete Block Design (BIBD) remained an unsolved problem in combinatorial design; also various construction techniques have been introduced to build the elements of BIBDs for specific parameters; no general method has been proposed to find a suitable structure for BIBDs. This paper aim at employing Finite Euclidean Geometry FEG (N,s) of N – dimensional space to construct balanced incomplete block design (BIBD). Also geometrical construction of FEG (2,2) BIBDs has been made. The results show that this technique proved a better method for constructing BIBD than other methods in terms of estimation of parameters to build the design structure.

scholarly journals Resolvable (r, λ)-designs and the Fisher inequality

1979 ◽  
Vol 28 (4) ◽  
pp. 471-478 ◽  
Author(s):  
S. A. Vanstone
Keyword(s):  
Block Design ◽  
Incomplete Block ◽  
Balanced Incomplete Block Design ◽  
Incomplete Block Design ◽  
Pairwise Balanced Designs ◽  
Balanced Designs ◽  
Similar Inequality ◽  
Balanced Incomplete Block

AbstractIt is well known that in any (v, b, r, k, λ) resolvable balanced incomplete block design that b≧ ν + r − l with equality if and only if the design is affine resolvable. In this paper, we show that a similar inequality holds for resolvable regular pairwise balanced designs ((ρ, λ)-designs) and we characterize those designs for which equality holds. From this characterization, we deduce certain results about block intersections in (ρ, λ)-designs.

scholarly journals Prime-number-assisted block-based neighbor discovery protocol in wireless sensor networks

2019 ◽  
Vol 15 (1) ◽  
pp. 155014771982624 ◽  
Author(s):  
Woosik Lee ◽  
Jong-Hoon Youn ◽  
Teukseob Song
Keyword(s):  
Prime Number ◽  
Block Design ◽  
Sensor Nodes ◽  
Neighbor Discovery ◽  
Incomplete Block ◽  
Balanced Incomplete Block Design ◽  
Incomplete Block Design ◽  
Block Based ◽  
Balanced Incomplete Block ◽  
Neighbor Discovery Protocol

During the initial deployment time, wireless sensors continually search their neighbors. The neighbor discovery is not an one-time event because the network topology can be changed anytime due to node mobility and failure. The neighbor discovery protocol helps sensor nodes to find neighboring sensors within their communication range. This study proposes a novel neighbor discovery protocol called the prime-number-assisted block-based neighbor discovery protocol, which intelligently changes the sensor schedules based on the greater common divisor of two sensors’ discovery cycle lengths. For example, for two sensors whose duty cycles are different, if the lengths of their discovery schedules are relatively prime, the prime-number-assisted block-based neighbor discovery protocol simply uses the balanced incomplete block design–based neighbor discovery protocol without adding any additional active slots; otherwise, it changes the original balanced incomplete block design–based schedule using a prime number. In this study, we compare the performances of prime-number-assisted block-based neighbor discovery protocol and other recently proposed neighbor discovery protocols (U-Connect, Disco, SearchLight, and Hedis) using a TOSSIM simulator. The experimental results confirm the superiority of prime-number-assisted block-based neighbor discovery protocol over other neighbor discovery protocols in terms of discovery latency and energy consumptions.

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.

Balanced Incomplete Block Design: Description, Case Study, and Implications for Practice

1995 ◽  
Vol 22 (2) ◽  
pp. 201-210 ◽  
Author(s):  
Bruce F. Campbell ◽  
Sohini Sengupta ◽  
Cielo Santos ◽  
Kate R. Lorig
Keyword(s):  
Block Design ◽  
Incomplete Block ◽  
Balanced Incomplete Block Design ◽  
Incomplete Block Design ◽  
Balanced Incomplete Block
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