Check of incompleteness due to proper motion in the UKIDSS dataset. The positional offsets in the UKIDSS J, H, and K images, relative to the reference Y image, were first computed, as well as the epoch differences between the pairs of observations. The maximum offset was selected and this quantity is plotted for each source against the relevant epoch difference. The red dots represent the 192 known L and T dwarfs in DwarfArchives.org, J< 17.5, within the UKIDSS footprint. The black dots are the objects in our new sample. On the basis of this plot, incompleteness due to proper motion is estimated to be ≪1%.