Exponential Bounds on the Number of Designs with Affine Parameters

被引：1

作者：

Clark, David ^{[1
]}

Jungnickel, Dieter ^{[2
]}

Tonchev, Vladimir D. ^{[1
]}

机构：

[1] Michigan Technol Univ, Dept Math Sci, Houghton, MI 49931 USA

[2] Univ Augsburg, Lehrstuhl Diskrete Math Optimierung & Operat Res, D-86135 Augsburg, Germany

来源：

JOURNAL OF COMBINATORIAL DESIGNS | 2010年 / 18卷 / 06期

关键词：

2-design; 3-design; resolvable design; finite affine geometry;

D O I：

10.1002/jcd.20256

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 [D. Jungnickel, V. D. Tonchev, Des Codes Cryptogr, published online: 23 May, 2009] 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, as well as resolvable designs with these parameters. An exponential lower bound is also proved for the number of non-isomorphic resolvable 3-designs with the same parameters as an affine geometry design whose blocks are the d-subspaces of AG(n, 2), for any 2 <= d <= n-1. (C) 2010 Wiley Periodicals, Inc. J Combin Designs 18: 475-487, 2010

引用

页码：475 / 487

页数：13

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