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Correction to: “Exponential bounds on the number of designs with affine parameters”
Author(s) -
Clark David,
Jungnickel Dieter,
Tonchev Vladimir D.
Publication year - 2011
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.20276
Subject(s) - mathematics , hyperplane , linear subspace , exponential function , affine transformation , combinatorics , discrete mathematics , combinatorial design , geometry , mathematical analysis
It is well known that the number of designs with the parameters of a classical design having as blocks the hyperplanes in PG ( n, q ) or AG ( n, q ), n ⩾3, grows exponentially. This result was extended recently [5] to designs having the same parameters as a projective geometry design whose blocks are the d ‐subspaces of PG ( n, q ), for any 2⩽ d ⩽ n − 1. In this paper, exponential lower bounds are proved on the number of non‐isomorphic designs having the same parameters as an affine geometry design whose blocks are the d ‐subspaces of AG ( n, q ), for any 2≤ d ≤ n − 1. Exponential bounds are also proved for the number of resolvable designs with these parameters. © 2011 Wiley Periodicals, Inc. J Combin Designs 19:156‐166, 2011