On the coexistence of conference matrices and near resolvable 2-(2k+1, k, k-1) designs

@article{Greig2006OnTC,
  title={On the coexistence of conference matrices and near resolvable 2-(2k+1, k, k-1) designs},
  author={Malcolm Greig and Harri Haanp{\"a}{\"a} and Petteri Kaski},
  journal={J. Comb. Theory, Ser. A},
  year={2006},
  volume={113},
  pages={703-711}
}
We show that a near resolvable 2-(2k + 1, k, k − 1) design exists if and only if a conference matrix of order 2k +2 does. A known result on conference matrices then allows us to conclude that a near resolvable 2-(2k + 1, k, k − 1) design with even k can only exist if 2k + 1 is the sum of two squares. In particular, neither a near resolvable 2-(21, 10, 9… CONTINUE READING