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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}  .

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