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 infinite series of designs over finite fields for arbitrary prime powers begin{document}$q$end{document} with parameters begin{document}$2text{-}(8,4,frac{(q^6-1)(q^3-1)}{(q^2-1)(q-1)};q)$end{document} as well as designs with parameters begin{document}$2text{-}(10,4,85λ;2)$end{document} , begin{document}$2text{-}(10,5,765λ;2)$end{document} , begin{document}$2text{-}(11,5,6205λ;2)$end{document} , begin{document}$2text{-}(11,5,502605λ;2)$end{document} , and begin{document}$2text{-}(12,6,423181λ;2)$end{document} for begin{document}$λ = 7,12,19,21,22,24,31,36,42,43,48,49,55,60,63$end{document} .