A 2-(22, 8, 4) Design Cannot Have a 2-(10, 4, 4) Subdesign

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

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A fast algorithm for the maximum clique problem

Discrete Applied Mathematics - Sixth Twente Workshop on Graphs and Combinatorial Optimization

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Abstract

The smallest BIBD, as for the number of points and blocks, whose existence is still undecided is 2-(22, 8, 4). Possible subconfigurations of such a design, namely 2-(10, 4, 4) designs, are here ruled out. The result is obtained by classifying all 2-(10, 4, 4) designs and trying to find 2-(22, 8, 4) designs by solving instances of the maximum clique problem.