Discontinuous molecular dynamics simulations are used to study the structure and relaxation of large, off-lattice, near-perfect, tri- and tetrafunctional polymer networks at a packing fraction of 0.43. The networks are constructed by end-linking freely jointed, tangent hard-sphere chains ranging in length from N = 20 to N = 150 and are then relaxed for 5-20 billion collisions. The simulation trajectories are used to calculate the radius of gyration and end-to-end distance of the network chains, the static structure factor of the cross-links, the mean-squared displacement of the cross-links and chain inner segments, the intermediate scattering function of the chains, and the elastic modulus of the network. The structure and properties of the networks are shown to depend heavily on the manner in which the network is initially constructed. The dynamics of the network cross-links and chain inner segments are similar to those of melt chains at short times and show evidence of spatial localization at long times. The results from the elastic moduli and long-time cross-link and chain displacement calculations indicate that entanglement constraints act in conjunction with cross-link constraints to reduce cross-link and chain mobility. The presence of entanglements appears to cause the magnitude of the elastic modulus to be larger than the affine/phantom model predictions.