Measuring 40x40cm, 16x16" is a common size for photo prints, art work and posters. The standard way to measure a print is by measuring width by height.
To get the best print result for 16x16", you'll need at least 1152 x 1152px and ideally 4800 x 4800px.
If you are looking for a frame with a mat for an 16x16" photo, choose the 20x20" (48x48cm) frame. The mat will have an 16x16" (40x40cm) opening.