The above numbers were obtained from random sprinkling of points into S^2.

The first five entries match those constructed from A018242, by explicitly applying each reorientation to a representative chirotope for each class of A018242, and grouping the chirotopes related by a permutation.

REFERENCES

J. Brunnemann and D. Rideout, "Oriented matroids—combinatorial structures underlying loop quantum gravity", Class.Quant.Grav. 27, 205008 (2010).

J. Richter-Gebert, "On the Realizability Problem of Combinatorial Geometries - Decision Methods", Ph.D. thesis, TH-Darmstadt 1992, 144 pages.