Title Parity restrictions for orthogonal arrays Sara Herke (The University of Queensland) Sara Herke, Nevena Francetic and Ian Wanless Algebra and Discrete Mathematics 11:00:00 2017-09-26 One of the biggest open questions in combinatorics is whether or not there exists a projective plane for non-prime power orders. There is a well-known correspondence between finite projective planes and orthogonal arrays with the maximum number of columns. We present a notion of parity of an orthogonal array and discuss parity restrictions that give some insight as to why it may be harder to build projective planes of order $n \equiv 2\mod4$, $n>2$, (which are widely believed not to exist) compared to other orders.