## Existence of near resolvable (v, k, k-1) BIBDs with k∈{9, 12, 16}

- R. Julian R. Abel
- Australasian J. Combinatorics
- 2017

@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} }

- Published 2006 in J. Comb. Theory, Ser. A
DOI:10.1016/j.jcta.2005.05.005

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

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