
LINKS

Table of n, a(n) for n=1..13.
O. Aichholzer, Order Types for Small Point Sets
O. Aichholzer, F. Aurenhammer and H. Krasser, Enumerating order types for small point sets with applications, In Proc. 17th Ann. ACM Symp. Computational Geometry, pages 1118, Medford, Massachusetts, USA, 2001. [Computes a(10)]
S. Felsner and J. E. Goodman, Pseudoline Arrangements. In: Toth, O’Rourke, Goodman (eds.) Handbook of Discrete and Computational Geometry, 3rd edn. CRC Press, 2018.
J. Ferté, V. Pilaud and M. Pocchiola, On the number of simple arrangements of five double pseudolines, arXiv:1009.1575 [cs.CG], 2010; Discrete Comput. Geom. 45 (2011), 279302.
Lukas Finschi, A Graph Theoretical Approach for Reconstruction and Generation of Oriented Matroids, A dissertation submitted to the Swiss Federal Institute of Technology, Zurich for the degree of Doctor of Mathematics, 2001.
L. Finschi, Homepage of Oriented Matroids
L. Finschi and K. Fukuda, Complete combinatorial generation of small point set configurations and hyperplane arrangements, pp. 97100 in Abstracts 13th Canadian Conference on Computational Geometry (CCCG '01), Waterloo, Aug. 1315, 2001.
J. E. Goodman and R. Pollack, Semispaces of configurations, cell complexes of arrangements, J. Combin. Theory, A 37 (1984), 257293.
D. E. Knuth, Axioms and hulls, Lect. Notes Comp. Sci., Vol. 606.
Alexander Pilz and Emo Welzl, Order on order types, Discrete & Computational Geometry, 59 (No. 4, 2015), 886922.
Manfred Scheucher, Hendrik Schrezenmaier, and Raphael Steiner, A Note On Universal Point Sets for Planar Graphs, arXiv:1811.06482 [math.CO], 2018.


FORMULA

Asymptotics: a(n) = 2^(Theta(n^2)). This is BachmannLandau notation, that is, there are constants n_0, c, and d, such that for every n >= n_0 the inequality 2^{c n^2} <= a(n) <= 2^{d n^2} is satisfied. For more information see e.g. the Handbook of Discrete and Computational Geometry.  Manfred Scheucher, Sep 12 2019
