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More on the plane of order 10

  • Jean François Maurras
Section III Combinatorial And Algebraic Aspects
Part of the Lecture Notes in Computer Science book series (LNCS, volume 388)

Abstract

We know that if the plane of order 10 contains a (3,1;21)t-design, it contains a 20-configuration defined in [2] (i.e. a 20-subset of the set of the points intersected by the lines in 0,2 or 4 points). Also if such a plane exists, it contains such a configuration. We investigate the relations between this 20-configuration and this (3,1;21)t-design.

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References

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    George Bernard Dantzig, Maximization of a linear function of variables subject tolinear inequalities, Chap XXI, Activity Analysis of Production and Allocation (T.C. Koopmans, ed.), New York: John Wiley and Sons, Inc., 1951.Google Scholar
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    Marshall Hall Jr., Configurations in a plane of order ten, Annals of Discrete Mathematics 6, 1980.Google Scholar
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    C.W.H. Lam and al., The nonexistence of ovals in a projective plane of order 10, Discrete Mathematics, Vol 45, No 2,3, July 1983.Google Scholar
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    C.W.H. Lam and al., The nonexistence of code words of weight 16 in a projective plane of order 10, J.C.T. serie A 42, 207–214 1986.CrossRefGoogle Scholar
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    J.F. Maurras, Sous-structures extrêmes dans les plans projectifs finis, cas impair, preprint G.R.T.C. Marseille, Janvier 1988.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Jean François Maurras
    • 1
  1. 1.G.R.T.C. C.N.R.S.Marseille Cedex 9

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