Using the existence of a special quadrisecant line, we show the ropelength of any nontrivial knot is at least 15.66. This improves the previously known lower bound of 12. Numerical experiments have found a trefoil with ropelength less than 16.372, so our new bounds are quite sharp.
"Quadrisecants give new lower bounds for the ropelength of a knot." Geom. Topol. 10 (1) 1 - 26, 2006. https://doi.org/10.2140/gt.2006.10.1