  The lattice stick number of a knot type is defined to be the minimal number
of straight line segments required to construct a polygon presentation of the
knot type in the cubic lattice. In this paper, we mathematically prove that the
trefoil knot $3_1$ and the figure-8 knot $4_1$ are the only knot types of
lattice stick number less than 15, which verifies the result from previous
numerical estimations on this quantity.
