Nontrivial t-designs over finite fields exist for all t

Arman Fazeli, Shachar Lovett, Alexander Vardy. Nontrivial t-designs over finite fields exist for all t. Journal of Combinatorial Theory, Series A, 127:149-160, 2014. [doi]

@article{FazeliLV14,
  title = {Nontrivial t-designs over finite fields exist for all t},
  author = {Arman Fazeli and Shachar Lovett and Alexander Vardy},
  year = {2014},
  doi = {10.1016/j.jcta.2014.06.001},
  url = {http://dx.doi.org/10.1016/j.jcta.2014.06.001},
  researchr = {https://researchr.org/publication/FazeliLV14},
  cites = {0},
  citedby = {0},
  journal = {Journal of Combinatorial Theory, Series A},
  volume = {127},
  pages = {149-160},
}