A superconducting La1.84Sr0.16CuO4 film patterned into a network of 100×100nm2 noninteracting square loops exhibits large magnetoresistance oscillations superimposed on a background which increases monotonically with the applied magnetic field. Neither the oscillations amplitude nor its temperature dependence can be explained by the Little-Parks effect. Conversely, a good quantitative agreement is obtained with a recently proposed model ascribing the oscillations to the interaction between thermally excited moving vortices and the oscillating persistent currents induced in the loops. Extension of this model, allowing for direct interaction of the vortices and antivortices magnetic moment with the applied field, accounts quantitatively for the monotonic background as well. Analysis of the background indicates that in the patterned film both vortices and antivortices are present at comparable densities. This finding is consistent with the occurrence of Berezinskii-Kosterlitz-Thouless transition in La1.84Sr0.16CuO4 films.