Third order Lovelock black branes in the presence of a nonlinear electromagnetic field

We consider third order Lovelock gravity coupled to an U(1) gauge field for which its Lagrangian is given by a power of Maxwell invariant. In this paper, we present a class of horizon flat rotating black branes and investigate their geometrical properties and the effect of nonlinearity on the solutions. We use some known formulas and methods to calculate thermodynamic and conserved quantities. Finally, we check the satisfaction of the first law of thermodynamics