This folder contains a full classification of the graphs with 6 and 7 vertices up to the last Henneberg step and the number of real embeddings (the 6-vertex case was already known).
We also provide a classification of the graphs with 8 vertices up to the last Henneberg step, resulting in the number of real embeddings for every graph which can be constructed with an H1 move in the final step (from now on H1-last).
For the graphs constructed with an H2 move in the final step (from now on H2-last), we provide the number of complex embeddings, except for the cases of G_128 and G_160, where we include also an achieved number of real embeddings (see https://arxiv.org/abs/1802.05860 for details).

The text files containing H1-last graphs have the following 2 columns:
edges of the graph- number of real embeddings

The text files containing H2-last graphs have the following 5 columns:
edges of the graph- mixed volume of sphere equations system- mixed volume of distance subsystems- number of complex embeddings - number of real embeddings
(In order to find an upper bound for distance subsystems we looked for square subsystems with n-4 variables. Some 8-vertex graphs do not contain such subsystems.)