The number of designs with geometric parameters grows exponentially

DOI10.1007/s10623-009-9299-6zbMath1215.05018OpenAlexW2095169408MaRDI QIDQ970530

Vladimir D. Tonchev, Dieter Jungnickel

Publication date: 19 May 2010

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10623-009-9299-6

zbMATH Keywords

designhyperplaneprojective geometry

Mathematics Subject Classification ID

Combinatorial aspects of block designs (05B05) Combinatorial structures in finite projective spaces (51E20)

Related Items (15)

A switching for all strongly regular collinearity graphs from polar spaces ⋮ Characterizing geometric designs. II. ⋮ Recent results on designs with classical parameters ⋮ The characterization problem for designs with the parameters of \(\mathrm{AG}_d(n,q)\) ⋮ New invariants for incidence structures ⋮ On the number of designs with affine parameters ⋮ Miklós-Manickam-Singhi conjectures on partial geometries ⋮ Remarks on polarity designs ⋮ Designs having the parameters of projective and affine spaces ⋮ A generalization of a result of Dembowski and Wagner ⋮ New strongly regular graphs from finite geometries via switching ⋮ Exponential bounds on the number of designs with affine parameters ⋮ Polarities, quasi-symmetric designs, and Hamada's conjecture ⋮ Correction to: “Exponential bounds on the number of designs with affine parameters” ⋮ Automorphism groups of designs with \(\lambda = 1\)

Cites Work

• A new bound on the number of designs with classical affine parameters
• On the p-rank of the incidence matrix of a balanced or partially balanced incomplete block design and its applications to error correcting codes
• The number of designs with classical parameters grows exponentially
• Polarities, quasi-symmetric designs, and Hamada's conjecture
• Quasi-symmetric \(2\text{-}(31,7,7)\) designs and a revision of Hamada's conjecture
• Automorphisms and isomorphisms of symmetric and affine designs
• Some characterizations of quasi-symmetric designs with a spread
• Bounds on the number of affine, symmetric, and Hadamard designs and matrices
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: The number of designs with geometric parameters grows exponentially