The density of Costas arrays and three-free permutations

We describe how 3-free permutations might be used to improve Davies's density result for Costas arrays. We associate both Costas arrays and 3-free permutations with a pair consisting of a lattice point and a hyperplane arrangement to establish relationships between the two and compare how the exponential decay predicted by bounds on the number of 3-free permutations compares with a claim of Drakakis.