Some new symmetric designs with parameters (64, 28, 12) (Q5939919)

The authors employed tactical decompositions to construct forty-six previously unknown mutually nonisomorphic \((64,28,12)\) designs that admit an action of the nonabelian group of order 21. The full automorphism groups and \(2\)-ranks for these designs were determined with the aid of electronic computation. The order of the largest such automorphism group is 168, and all the designs have a \(2\)-rank of \(26\) or \(27\).