Linear quadratic games on very large dense networks are modelled with discrete time linear quadratic graphon field games with Q-noise. In such a game, the agents are interconnected via an undirected network with one agent per node. Brownian motion which is correlated over nodes affects each agent. The limit of the finite-sized linear quadratic network tracking game in discrete time is formulated, and it is shown that under the proper assumptions, the game has a graphon limit system with Q-noise. Then, the optimal control of the discrete time system is found in closed-form and the Nash equilibrium behavior of the game is demonstrated numerically. The infinite time horizon discounted case is also analyzed, and a closed form feedback solution is presented in the special case where the underlying graphon is finite rank.