# An algorithm for counting arcs in higher-dimensional projective space

@inproceedings{Isham2021AnAF, title={An algorithm for counting arcs in higher-dimensional projective space}, author={Kelly Isham}, year={2021} }

An n arc in (k − 1)-dimensional projective space is a set of n points so that no k lie on a hyperplane. In 1988, Glynn gave a formula to count n-arcs in the projective plane in terms of simpler combinatorial objects called superfigurations. Several authors have used this formula to count n-arcs in the projective plane for n ≤ 10. In this paper, we determine a formula to count n-arcs in projective 3-space. We then use this formula to give exact expressions for the number of n-arcs in P3(Fq) for…

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