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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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  • Mandal, S.
  • Ghosh, D.K.
  • Sharma, R.K.
  • Bagui, S.C.

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.

Suggested Citation

  • Mandal, S. & Ghosh, D.K. & Sharma, R.K. & Bagui, S.C., 2008. "A complete class of balanced incomplete block designs [beta] (7, 35, 15, 3, 5) with repeated blocks," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3338-3343, December.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:18:p:3338-3343
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    1. D. K. Ghosh & S. B. Shrivastava, 2001. "A class of BIB designs with repeated blocks," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(7), pages 821-833.
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