Minimum 6-connected graph on 200 vertices 
Find the samllest number of edges in 6-vertex-connected graph on 200 vertices.

I think that the answer is 600 , using the fact that $\delta(G) \geq \kappa(G)$.
But the smallest 6-vertex-connected graph that I could come up with is $K_{6,194}$ (the complete bipartite graph with size 6 and 194) , which sounds like far from optimal...
A hint/intuition will be very helpful .

As JMoritz noted : 
I would think that the graph with adjacencies defined as $v_i$ is adjacent to $v_j$ with $j=((−1+i+n) \ mod \ 200)+1,$ $n∈\{−3,−2,−1,1,2,3\}$. (I.e. $v_4$ is adjacent to each of $v_1,v_2,v_3,v_5,v_6,v_7$ whereas $v_1$ is adjacent to $v_{198},v_{199},v_{200},v_2,v_3,v_4$). Each vertex has exactly 6 edges, and you can check that it is in fact six-connected(the easiest way is to see that thee are 6 vertex disjoint paths between every two vertices, then by Menger's we could conclude that the graph is 6 connected)
