I don't have a 1/16" ruler. However Omnigrid makes a 3x18 and a 4x8" ruler. Both of these are marked for 1/8".
I did a quilt that was based on 1/16" measurements with some friends. We just estimated the half way mark tween the 1/8" marks. That experience taught us what we never want to do again ... make another quilt with 1/16" incremental measurements.
Hope this helps.
ali