  Using the possibility of computationally determining points on a finite cover
of a unirational variety over a finite field, we determine all possibilities
for direct Gorenstein linkages between general sets of points in P^3 over an
algebraically closed field of characteristic 0. As a consequence we show that a
general set of d points is glicci (that is, in the Gorenstein linkage class of
a complete intersection) if d <= 33 or d=37,38. Computer algebra plays an
essential role in the proof. The case of 20 points had been an outstanding
problem in the area for a dozen years.
