Realizability of a 23-point set with no empty hexagon and no 7-gon

Construct a planar point set of 23 points in general position that contains neither an empty convex hexagon (a 6-hole) nor a convex 7-gon, or prove that no such point set exists, thereby determining whether the combinatorial examples (signotopes) on 23 elements witnessing this property are realizable as actual point sets.

Background

The paper proves that every set of 24 points in the plane in general position contains either a 6-hole or a 7-gon, and it further shows that in the combinatorial setting of signotopes this bound is sharp: there exist signotopes on 23 elements with neither a 6-hole nor a 7-gon.

However, the authors were unable to realize any of these signotopes as actual point sets in the plane: all tested candidates were shown non-realizable by bi-quadratic final polynomials. This leaves open whether a 23-point geometric point set avoiding both structures exists or whether the lower bound in the geometric setting is strictly larger than in the combinatorial signotope setting.