Book contents
- Frontmatter
- Contents
- Preface
- Introduction
- On maximum size anti-Pasch sets of triples
- Some simple 7–designs
- Inscribed bundles, Veronese surfaces and caps
- Embedding partial geometries in Steiner designs
- Finite geometry after Aschbacher's Theorem: PGL(n, q) from a Kleinian viewpoint
- The Hermitian function field arising from a cyclic arc in a Galois plane
- Intercalates everywhere
- Difference sets: an update
- Computational results for the known biplanes of order 9
- A survey of small embeddings for partial cycle systems
- Rosa triple systems
- Searching for spreads and packings
- A note on Buekenhout-Metz unitals
- Elation generalized quadrangles of order (q2, q)
- Uniform parallelisms of PG(3, 3)
- Double-fives and partial spreads in PG(5, 2)
- Rank three geometries with simplicial residues
- Generalized quadrangles and the Axiom of Veblen
- Talks
- Participants
Searching for spreads and packings
Published online by Cambridge University Press: 04 November 2009
Book contents
- Frontmatter
- Contents
- Preface
- Introduction
- On maximum size anti-Pasch sets of triples
- Some simple 7–designs
- Inscribed bundles, Veronese surfaces and caps
- Embedding partial geometries in Steiner designs
- Finite geometry after Aschbacher's Theorem: PGL(n, q) from a Kleinian viewpoint
- The Hermitian function field arising from a cyclic arc in a Galois plane
- Intercalates everywhere
- Difference sets: an update
- Computational results for the known biplanes of order 9
- A survey of small embeddings for partial cycle systems
- Rosa triple systems
- Searching for spreads and packings
- A note on Buekenhout-Metz unitals
- Elation generalized quadrangles of order (q2, q)
- Uniform parallelisms of PG(3, 3)
- Double-fives and partial spreads in PG(5, 2)
- Rank three geometries with simplicial residues
- Generalized quadrangles and the Axiom of Veblen
- Talks
- Participants
Summary
Abstract
New algorithms are presented for finding spreads and packings of sets with applications to combinatorial designs and finite geometries. An efficient deterministic method for spread enumeration is used to settle several existence problems for t-designs and partial geometries. Randomized algorithms based on tabu search are employed to construct new Steiner 5-designs and large sets of combinatorial designs. In particular, partitions are found of the 4-subsets of a 16-set into 91 disjoint affine planes of order 4.
- Type
- Chapter
- Information
- Geometry, Combinatorial Designs and Related Structures , pp. 161 - 176Publisher: Cambridge University PressPrint publication year: 1997
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