It is shown that a 4-(12,6,6) design, if it exists, must be rigid. The intimate relationship of such a design with 4-(12,5,4) designs and 5-(12,6,3) designs is presented and exploited. In this endeavor we found: (i) 30 nonisomorphic 4-(12,5,4) designs; (ii) all cyclic 3-(11,5,6) designs; (iii) all 5-(12,6,3) designs preserved by an element of order three fixing no points and no blocks; and (iv) all 5-(12,6,3) designs preserved by an element of order two fixing 2 points.
Department, Program, or Center
Center for Advancing the Study of CyberInfrastructure
Australasian Journal of Combinatorics 7 (1993) 3-20
RIT – Main Campus