Edge deletion preserving the diameter of the hypercube

We give upper and lower bounds to the number un− (Qn) of edges that one can remove from a hypercube without altering its diameter, namely: (n − 2)2n − 1 − (n⌊n2⌋) + 2 ⩽ un−(Qn) ⩽(n − 2)2n − 1 + 1 − ⌈ (2n − 1)(2n − 1)⌉.