New 2-designs over finite fields from derived and residual designs.

Based on the existence of designs for the derived and residual parameters of admissible parameter sets of designs over finite fields we obtain a new in finite series of designs over finite fields for arbitrary prime powers q with parameters 2-(8, 4, (q(6)-1)(q(3)-1)/(q(2)-1)(q-1) ; q) as well as designs with parameters 2-(10, 4, 85 lambda; 2), 2-(10, 5, 765 lambda; 2), 2-(11, 5, 6205 lambda; 2), 2-(11, 5, 502605 lambda; 2), and 2-(12, 6, 423181 lambda; 2) for lambda = 7, 12, 19, 21, 22, 24, 31, 36, 42, 43, 48, 49, 55, 60, 63.