Before revision:  Surprisingly, for d=4,5,6 the stretched grid yields better bounds than the stretched diagonal (unlike for all cases k=0 and for the case (d,k)=(3,1), in which both point sets yield the same bound).
After revision:  We provide strong evidence that, surprisingly, for d=4,5,6 the stretched grid yields better bounds than the stretched diagonal (unlike for all cases k=0 and for the case (d,k)=(3,1), in which both point sets yield the same bound).