# Reference on the classification of (low rank) Gorenstein rings over $\mathbb{C}$

I am interested in the question of the classification of (low rank) Gorenstein rings over $\mathbb{C}$. The socle of a local algebra is the annihilator of its maximal ideal. A commutative local ring is called Gorenstein iff its socle is 1-dimensional. Here, “rank” means the dimension of the algebra as a vector space.

A classification of low rank (<7) algebra can be found in http://math.mit.edu/~poonen/papers/dimension6.pdf and so do the Gorenstein rings. But I didn’t find further results. Is there any reference?