Note that the auther of the latter paper formulated the calculation of P(n, d) as a binary integer program with linear/quadratic constraints and found its value
for n ∈ {5, 6}. By using a solver (Gurobi Optimization Inc), the values of P(5, d) for d ∈ {3, 4, 5, 6} and P(6, d) for d ∈ {4, 5, . . . , 10} has been found successfully . But the solver has not been able to find the optimal value of P(6, 3) even after several weeks of computation. The solver has found a heuristic solution of cardinality 102 improving the lower bound on P(6, 3) from the previous value of 90. Click
here to see 720 constraints of the optimization problem corresponding to P(6,3).