Modified partially balanced incomplete block (PBIB) designs having higher associate classes are presented by adopting the concept of transposing the basic (incidence) matrix in this research manuscript. For this purpose, the structure of PBIB design based on the hamming distance for each literal of K-Map be treated as a basic (incidence) matrix. Construction methodology, an association scheme, and all kinds of efficiency factors as well as the overall efficiency factor of all existing modified PBIB designs are presented in the successive sections of this paper. From a practical point of view, an illustration of a particular design is also visualized through understanding the scheme.

partially balanced incomplete block design, K-Map, hamming distance, primal and dual, group, transpose.

Received: October 1, 2022; Accepted: November 25, 2022; Published: January 4, 2023

How to cite this article: Gurinder Pal Singh and Davinder Kumar Garg, Modified partially balanced incomplete block designs having higher associate classes by using the literals of K-Maps, Far East Journal of Theoretical and Applied Sciences 1 (2022), 25-32. http://dx.doi.org/10.17654/TAS2022003

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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