Before revision:  This construction is more sparse than the most recent work ( Buchin, Ol\`ah, and Har-Peled 2018) which proves the existence of (1+\epsilon)k-robust t-spanners with n\log^{O(d)} n edges.
After revision:  This construction is sparser than the recent constructions of Buchin, Ol\`ah, and Har-Peled 2018) which proves the existence of (1+\epsilon)k-robust t-spanners with n\log^{O(d)} n edges.