Ben Green and Terence Tao showed that for all sufficiently large point sets (that is, formula_97 for some suitable choice of formula_98), the number of ordinary lines is indeed at least formula_92. Furthermore, when formula_1 is odd, the number of ordinary lines is at least formula_101, for some constant formula_18. Thus, the constructions of Böröczky for even and odd (discussed above) are best possible. Minimizing the number of ordinary lines is closely related to the orchard-planting problem of maximizing the number of three-point lines, which Green and Tao also solved for all sufficiently large point sets.