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Combinatorial Mathematics III pp 83–89Cite as

Computer assisted generation of difference blocks

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 452))

Abstract

The Stanton-Mullin classification of BIBDs into (v,k) families has been extended by Collens to produce BIBSYS, an automatic system for storage, retrieval, and generation of BIBDs. The resulting tables show quite a few gaps in our knowledge concerning existence of early entries in the table. This paper describes an algorithm which has been successfully used to generate initial difference blocks which produce various designs by modular addition.

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References

  1. R. A. Fisher and F. Yates, Statistical tables for biological, agricultural, and medical research Sixth edition, Oliver and Boyd, London (1963).

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  2. M. Hall Jr., Combinatorial Theory Blaisdell, Waltham, Mass. (1967)

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  3. R. C. Mullin and R. J. Collens, Near block designs and BIBDs Proc. Fifth South-eastern Conference on Combinatorics, Graph Theory, and Computing, Boca Raton (1974), in press.

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  4. C. R. Rao, A study of BIB designs with replications r=11 to 15 Sankhya (A) 23, 117–127 (1961).

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  5. D. A. Sprott, Listing of BIB designs with r=16 to 20 Sankhya (A) 24, 203–204 (1962).

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  6. R. G. Stanton and R. J. Collens, A computer system for research on the family classification of BIBDs Proc. International Conference on Combinatorics, Rome (1973), in press.

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  7. R. G. Stanton and R. C. Mullin, Classification and embedding of BIBDs Sankhya (A) 30, 91–100 (1968).

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  8. K. Takeuchi, A table of difference sets generating balanced incomplete block designs, Rep. Stat. Appl. Res., JUSE 10, 48 (1963)

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Manitoba, Winnipeg, Canada

    R. J. Collens & R. G. Stanton

  2. Department of Mathematics, University of Newcastle, Newcastle, New South Wales

    R. J. Collens & R. G. Stanton

Authors
  1. R. J. Collens
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  2. R. G. Stanton
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Editor information

Anne Penfold Street Walter Denis Wallis

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© 1975 Springer-Verlag

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Collens, R.J., Stanton, R.G. (1975). Computer assisted generation of difference blocks. In: Street, A.P., Wallis, W.D. (eds) Combinatorial Mathematics III. Lecture Notes in Mathematics, vol 452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069546

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  • DOI: https://doi.org/10.1007/BFb0069546

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07154-9

  • Online ISBN: 978-3-540-37482-4

  • eBook Packages: Springer Book Archive

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