Before revision:  The best known upper bounds for this problem are f_3(n)=O(n^{1.22 However, no lower bound besides the trivial bound f_d(n) \geq n is known to this date .
After revision:  The best known upper bounds for this problem are f_3(n)=O(n^{1.22 However, no non-trivial lower bound is known to this date .