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A complete class of balanced incomplete block designs [beta] (7, 35, 15, 3, 5) with repeated blocks

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  • Design

Abstract

Raghavarao, Federer and Schwager [Raghavarao, D., Federer, W.T., Schwager, S.J., 1986. Characteristics for distinguishing among balanced incomplete block designs with repeated blocks. Journal of Statistical Planning and Inference 13, 151-163] obtained a class of balanced incomplete block (BIB) designs [beta] (7, 21, 9, 3, 3), where nine out of ten BIB designs are of repeated blocks. Ghosh and Shrivastava [Ghosh, D.K., Shrivastava, S.B., 2001. A class of BIB designs with repeated blocks. Journal of Applied Statistics 28, 821-833] obtained another class of BIB designs [beta] (7, 28, 12, 3, 4) with repeated blocks where fourteen out of fifteen BIB designs are of repeated blocks. In this article we present a complete class of BIB designs [beta] (7, 35, 15, 3, 5) where one BIB design has distinct blocks while the remaining thirty designs are of repeated blocks. These thirty-one BIB designs are compared on the basis of the number of repeated blocks and the frequencies of variance of block effect contrasts. Although the parameters of the thirty-one BIB designs are the same, some of them are found to be isomorphic design, and hence they are new solutions of the given plan.

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