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Research Article Open access CC BY 4.0

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

U. P. Akra, S. S. Akpan, T. A. Ugbe, O. E. Ntekim

Asian Journal of Probability and Statistics · pp. 47–59 · Published 7 Apr 2021

10.9734/ajpas/2021/v11i430274

Abstract

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.

Block design BIBD geometry and Euclidean geometry

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