There are \(270,474,142\) Nonisomorphic \(2-(9, 4,6)\) Designs

Patric R. J. Ostergard 1
1 Department of Computer Science and Engineering Helsinki University of Technology P.O. Box 5400 02015 HUT, Finland

Abstract

We enumerate the 2-\((9,4,6)\) designs and find \(270,474,142\) non-isomorphic such designs in a backtrack search. The sizes of their automorphism groups vary between \(1\) and \(360\). Out of these designs, \(19,489,464\) are simple and \(2,148,676\) are decomposable.