New 2-designs over finite fields from derived and residual designs
Michael Braun, Michael Kiermaier, Reinhard Laue · Advances in Mathematics of Communications · 2018
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 $q$ with parameters $2\text{-}(8,4,\frac{(q^6-1)(q^3-1)}{(q^2-1)(q-1)};q)$ as well as designs with parameters $2\text{-}(10,4,85λ;2)$, $2\text{-}(10,5,765λ;2)$, $2\text{-}(11,5,6205λ;2)$, $2\text{-}(11,5,502605λ;2)$, and $2\text{-}(12,6,423181λ;2)$ for $λ = 7,12,19,21,22,24,31,36,42,43,48,49,55,60,63$.