Here we introduce two simple models: simple cubic random packing and random packing by Hamming distance. Consider the packing density γ d of dimension d by cubic random packing. From computer simulations up to dimension 11, γ d+1/γ d seems to approach 1. Also, we give simulation results for random packing by Hamming distance and discuss the behavior of packing density when dimensionality is increased. For the case of Hamming distances of 2 or 3, d–α fits the simulation results of packing density where α is an empirical constant. The variance of packing density is larger when k is even and smaller when k is odd, where k represents Hamming distance.
