For each h-vector hV in L for a Gorenstein collection as in of Proposition 4.1, we randomly choose a point J in HCh and check whether this point has tangent dimension as predicted by the dimension formula of Proposition 4.2 of Twenty Points in P^3.
i1 : S=ZZ/10009[x_0..x_3];(L1,L2)=listhVectors 1;
i3 : time checkDimensionsHCG(L1|L2,S)
-- used 0.0549515 seconds
o3 = Tally{true => 7}
o3 : Tally