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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Steiner systems $S(5,6,v)$ with $v=72$ and $84$


Authors: M. J. Grannell, T. S. Griggs and R. A. Mathon
Journal: Math. Comp. 67 (1998), 357-359
MSC (1991): Primary 05B05
Supplement: Additional information related to this article.
MathSciNet review: 1451323
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Abstract: It is proved that there are precisely 4204 pairwise non-isomorphic Steiner systems $S(5,6,72)$ invariant under the group $\mathrm{PSL}_2(71)$ and which can be constructed using only short orbits.

It is further proved that there are precisely 38717 pairwise non-isomorphic Steiner systems $S(5,6,84)$ invariant under the group $\mathrm{PSL}_2(83)$ and which can be constructed using only short orbits.


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Additional Information

M. J. Grannell
Affiliation: Department of Mathematics and Statistics, University of Central Lancashire, Preston PR1 2HE, United Kingdom

T. S. Griggs
Affiliation: Department of Mathematics and Statistics, University of Central Lancashire, Preston PR1 2HE, United Kingdom

R. A. Mathon
Affiliation: Department of Computer Science, University of Toronto, Toronto, Ontario, Canada M5S 1A4

DOI: http://dx.doi.org/10.1090/S0025-5718-98-00924-7
PII: S 0025-5718(98)00924-7
Received by editor(s): April 5, 1996
Article copyright: © Copyright 1998 American Mathematical Society