Abstract
We define the classical covering number N(t,k,v), and indicate what is currently known in this area. Then we provide a method which obtains some results on one of the difficult outstanding problems, namely, the value of N(3,4, 12a+7).
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References
W.H. Mills, On the Covering of Triples by Quadruples, Proc. Fifth Southeastern Conference on Combinatorics, Graph Theory and Computing, (Utilitas, Winnipeg, 1975), 563–581.
W.H. Mills, Covering Designs I: Coverings by a Small Number of Subsets, Ars Combin. 8 (1979), 199–315.
R.G. Stanton, J.G. Kalbfleisch, R.C. Mullin, Covering and Packing Designs, Proc. 2nd Chapel Hill Conference on Combinatorial Mathematics and its Applications, (Univ. North Carolina, Chapel Hill, 1970), 428–450.
R.M. Wilson, Construction and Uses of Pairwise-balanced Designs, Proc. NATO Advanced Study Inst. on Combinatorics, Nijenrode Castle, Bruekelen, Netherlands (1974), 19–42.
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© 1980 Springer-Verlag
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Stanton, R.G., Mullin, R.C. (1980). Some new results on the covering numbers N(t,k,v). In: Robinson, R.W., Southern, G.W., Wallis, W.D. (eds) Combinatorial Mathematics VII. Lecture Notes in Mathematics, vol 829. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088899
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DOI: https://doi.org/10.1007/BFb0088899
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