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Next: Introduction

Partitioned Steiner 5-Designs

Reinhard Laue, Alfred Wassermann,
University of Bayreuth, Germany


Orbits of $PSL(2,p)$ on 6-element subsets of the projective line with prescribed non-trivial stabilizer are described. A refinement of cross-ratio computations to $PSL(2,p)$ orbits allows to determine the orbits on 5-element subsets that they cover. Then Steiner $5$-$(p+1,6,1)$ designs are assembled from them. In particular, there is one isomorphism type of $5$-$(48,6,1)$ designs that consists of $PSL(2,p)$ orbits of the same size, each being a $3$-$(48,6,30)$ design. There are 7 isomorphism types of $5$-$(84,6,1)$ designs of this type. Generally, Steiner $5$-$(p+1,6,1)$ designs with such an orbit partition may only exist if $p\equiv 48,\ 84\ mod \ 180$.

N.N. 2002-02-25