Enumeration of 2-(9, 3, ) Designs and Their Resolutions

Authors: Östergård P.R.J.¹; Kaski P.²

Source: Designs, Codes and Cryptography, Volume 27, Numbers 1-2, October 2002 , pp. 131-137(7)

Publisher: Springer

Abstract:

We consider 2-(9, 3, ) designs, which are known to exist for all 1, and enumerate such designs for = 5 and their resolutions for 3 5, the smallest open cases. The number of nonisomorphic such structures obtained is 5 862 121 434, 426, 149 041, and 203 047 732, respectively. The designs are obtained by an orderly algorithm, and the resolutions by two approaches: either by starting from the enumerated designs and applying a clique-finding algorithm on two levels or by an orderly algorithm.

Keywords: automorphism group; BIBD; oderly algorithm; resolved design

Language: English

Document Type: Research article

Affiliations: 1: Department of Electrical and Communications Engineering, Helsinki University of Technology, P.O. Box 3000, 02015 HUT, Finland patric.ostergard@hut.fi 2: Department of Computer Science and Engineering, Helsinki University of Technology, P.O. Box 5400, 02015 HUT, Finland petteri.kaski@hut.fi

Publication date: 2002-10-01

• In this: publication
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• In this Subject: Computer Science ,  Mathematics and Statistics
• By this author: Östergård P.R.J. ;  Kaski P.

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