Construction of new symmetric designs with parameters (70,24,8) (Q687106)

The first symmetric design with parameters \((70,24,8)\) was constructed by \textit{Z. Janko} and \textit{Tran van Trung} [``The existence of a symmetric block design for (70,24,8)'', Mitt Math. Semin. Giessen 165, 17-18 (1984; Zbl 0571.05005)]; this design is self-dual and has a group of order 42 as its full automorphism group. The author constructs (70,24,8) designs with a considerably larger group, i.e., an extension of the elementary abelian group of order 8 with the nonabelian group of order 21; up to duality and isomorphism, there are exactly 5 such designs for which the automorphism of order 7 operates fixed-point-free.