The question is discussed whether a configuration (vr, bk) (i.e. is a finite incidence structure of v points and b lines such that each point lies on r lines, each line contains k points and two different points are connected at most once) can be drawn in the rational Euclidean plane as a system of v points and b lines. In the first part a historical survey is given concerning configurations v3 and (124,163) whereas the second part reports on those results obtained during the last years by means of new computational methods.
Gropp, H. (1997). Configurations and their realization. Discrete Mathematics, 174(1–3), 137–151. https://doi.org/10.1016/S0012-365X(96)00327-5