Points := [[Rand(9,9)  N In 1..3]  S In 1..25];
Use QQ[x,y,z];
I := IdealOfPoints(Points);
QuotientBasis(I);  power products underneath the DegRevLex reduced GBasis
[1, z, z^2, z^3, z^4, y, yz, yz^2, yz^3, y^2, y^2z, y^2z^2, y^3, x,
xz, xz^2, xz^3, xy, xyz, xyz^2, xy^2, x^2, x^2z, x^2y, x^3]

Use QQ[x,y,z], Lex;
I := IdealOfPoints(Points);
QuotientBasis(I);  power products underneath the Lex reduced GBasis
[1, z, z^2, z^3, z^4, z^5, z^6, z^7, z^8, z^9, z^10, z^11, z^12, z^13,
y, yz, yz^2, yz^3, yz^4, yz^5, yz^6, y^2, y^2z, y^2z^2, y^2z^3]

