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Lattice basis reduction can be used to solve linear systems of equations with 0,1-vectors. These arise for example in the construction of simple t-designs with prescriped automorphism group.
I'm involved in the development of the software package DISCRETA.The first simple 7-designs with small parameters were presented in Springer LNCS 948, pp.131-145 (abstract) and in Bayreuther Mathematische Schriften.
Here is a BibTeX-file containing the citations which are used in our papers.For an introduction to the subject see an article in Spektrum der Wissenschaft, May 1996: "Lotto, Schulmädchen und Versuchsplanung - eine Entdeckung in der Designtheorie". The pictures of this article can be downloaded here:
More information on recently found simple t-designs contain the
pages of
Anton Betten
and Prof. Dr. Reinhard
Laue.
Nearly everything about designs is contained in
The CRC HANDBOOK of COMBINATORIAL DESIGNS.
Designs in real life situations are
of increasing importance.
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