We present the analysis of the planetary microlensing event MOA-2016-BLG-319 .
The event light curve is characterized by a brief ( \sim 3 days ) anomaly near the peak produced by minor-image perturbations .
From modeling , we find two distinct solutions that describe the observed light curve almost equally well .
From the investigation of the lens-system configurations , we find that the confusion in the lensing solution is caused by the degeneracy between the two solutions resulting from the source passages on different sides of the planetary caustic .
These degeneracies can be severe for major-image perturbations but it is known that they are considerably less severe for minor-image perturbations .
From the comparison of the lens-system configuration with those of two previously discovered planetary events , for which similar degeneracies were reported , we find that the degeneracies are caused by the special source trajectories that passed the star-planet axes at approximately right angles .
By conducting a Bayesian analysis , it is estimated that the lens is a planetary system in which a giant planet with a mass M _ { p } = 0.62 ^ { +1.16 } _ { -0.33 } ~ { } M _ { J } ( 0.65 ^ { +1.21 } _ { -0.35 } ~ { } M _ { J } ) is orbiting a low-mass M-dwarf host with a mass M _ { h } = 0.15 ^ { +0.28 } _ { -0.08 } ~ { } M _ { \odot } .
Here the planet masses in and out of the parentheses represent the masses for the individual degenerate solutions .
The projected host-planet separations are a _ { \perp } \sim 0.95 au and \sim 1.05 au for the two solutions .
The identified degeneracy indicates the need to check similar degeneracies in future analyses of planetary lensing events with minor-image perturbations .