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# Partitioned Steiner 5-Designs

Reinhard Laue, Alfred Wassermann,
University of Bayreuth, Germany

### Abstract:

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

N.N. 2002-02-25

University of Bayreuth -