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BIBDs with κ = 6 and λ = 1

In: Computational and Constructive Design Theory

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  • W. H. Mills

    (Institute for Defense Analyses)

Abstract

Balanced incomplete block designs, or BIBDs, have been studied for many years. In a famous 115 page paper Haim Hanani completely settled the existence question for BIBDs with block size less than 6. In the same paper he settled this question for block size 6 and λ > 1. However when the block size is 6 and λ = 1 the whole question becomes much more difficult. In the present paper we discuss the work that has been done on this. There are, at present, 55 values of υ for which the existence of such a design is in doubt. We will show how the remaining values of υ are handled.

Suggested Citation

  • W. H. Mills, 1996. "BIBDs with κ = 6 and λ = 1," Springer Books, in: W. D. Wallis (ed.), Computational and Constructive Design Theory, chapter 0, pages 189-226, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4757-2497-4_8
    DOI: 10.1007/978-1-4757-2497-4_8
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