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.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
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.
Marshall Hall Jr., Configurations in a plane of order ten, Annals of Discrete Mathematics 6, 1980.
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.
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.
F.J. MacWilliams and N.J.A. Sloane and J.G. Thompson, On the existence of a projective plane of order 10, J.C.T., Vol. 14, No. 1, January 1973.
J.F. Maurras, Sous-structures extrêmes dans les plans projectifs finis, cas impair, preprint G.R.T.C. Marseille, Janvier 1988.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1989 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Maurras, J.F. (1989). More on the plane of order 10. In: Cohen, G., Wolfmann, J. (eds) Coding Theory and Applications. Coding Theory 1988. Lecture Notes in Computer Science, vol 388. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0019861
Download citation
DOI: https://doi.org/10.1007/BFb0019861
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51643-9
Online ISBN: 978-3-540-46726-7
eBook Packages: Springer Book Archive