Non-existence conjecture for bipartite diameter-3 defect-4 graphs

Let $d\ge 6$. A bipartite $(d,3,-4)$-graph is a bipartite graph of degree $d$, diameter $3$, and defect $4$.

Non-existence conjecture. There is no bipartite $(d,3,-4)$-graph with $d\ge 6$.

The conjecture extends the paper's proved non-existence result for bipartite $(7,3,-4)$-graphs and its observations concerning the cases $d=5$ and $d=6$. It asserts that bipartite graphs of diameter $3$ and defect $4$ do not exist in any degree at least $6$.