All 2-(21, 7, 3) designs are residual (Q1281152)

While quasi-residual symmetric \(2\)-\((v,k,\lambda)\) designs for \(\lambda= 1, 2\) are in fact residual the general situation is different. The author reports that there exist 18920 isomorphism types of \(2\)-\((16,6,3)\) designs of which only 1305 are residual. By computer search the author establishes that the residual designs of the \(2\)-\((31,10,3)\) designs comprise all \(2\)-\((21,7,3)\) designs, in total 3809 isomorphism types.