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

Authors:
Patric R. J. Östergård;Petteri Kaski
Affiliations:
Department of Electrical and Communications Engineering, Helsinki University of Technology, P.O. Box 3000, 02015 HUT, Finland patric.ostergard@hut.fi;Department of Computer Science and Engineering, Helsinki University of Technology, P.O. Box 5400, 02015 HUT, Finland petteri.kaski@hut.fi
Venue:
Designs, Codes and Cryptography
Year:
2002

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Abstract

We consider 2-(9, 3, λ) designs, which are known to exist for all λ ≥ 1, andenumerate such designs for λ = 5 and their resolutions for 3 ≤ λ ≤ 5, the smallestopen cases. The number of nonisomorphic such structures obtained is 5 862 121 434, 426, 149 041, and 203 047732, 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 anorderly algorithm.