This paper studies sparse packetized predictive control (PPC) for a feedback loop closed over a digital communication channel with time delay and bounded packet dropouts. In the considered networked control system (NCS), the channel is located between the controller and the actuator of a linear time-invariant (LTI) plant. We analyze the system under two PPC strategies. In one case, the controller computes each control packet by solving a sparsity-promoting unconstrained ℓ-ℓ optimization problem. In the other case, the optimization based on which the controller performs is an ℓ -constrained ℓ0 problem. We utilize effective approaches for solving these optimization problems. Moreover, we establish practical and asymptotic stability conditions for unconstrained ℓ -ℓ and ℓ-constrained ℓ0 sparse PPCs, respectively. We show that to maintain stability while increasing the channel delay, the proposed sparse PPC strategies necessitate increasing the upper bound on size of the control packet sequences. We demonstrate, through simulation, that when the channel delay is higher, the controllers designed according to the proposed methods can bring the expected stability properties to the system but with worse performance.