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Construction of balanced incomplete block designs using cyclic shifts. (English) Zbl 1321.05020
Among numerous experimental designs the most comfortable and congenial are the combinatorial designs and the balanced incomplete block designs of them are highly practicable. And so the developing of several constructional methods of these BIB designs became a compulsion. This field of combinatorial designs was originated by Fisher and Yates and much developed by R. C. Bose and further extended to many ramifications in the field. These BIB designs are defined as: \(v\) elements are grouped into \(b\) blocks of equal size \(k\) such that each element occurs for \(r\) times and each pair occurs for \(\lambda\) times. The parametric relations satisfying these relations can be seen in the literature. Constructional methods were given by many authors like Bose, Shrikhande, Raghavarao, and so many others as shown in the paper. In the present paper the authors produce some infinite series of these designs by the method of cyclic shifts and hence it is very interesting. The authors ingeniously developed eleven such distinct infinite series of these designs.
MSC:
05B05 Combinatorial aspects of block designs
62K10 Statistical block designs
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