Non-geometric distance-regular graphs of diameter at least $3$ with smallest eigenvalue at least $-3$

In this paper, we classify non-geometric distance-regular graphs of diameter at least $3$ with smallest eigenvalue at least $-3$. This is progress towards what is hoped to be an eventual complete classification of distance-regular graphs with smallest eigenvalue at least $-3$, analogous to existing classification results available in the case that the smallest eigenvalue is at least $-2$.