Here we give a braid representation of each knot. These were taken from [1], which gives the minimum length braid in each case. In all cases except the knot 10136, this also gives the number of strands. For that knot, we also give a braid with the minimum number of strands, taken from [2]. For 11 crossing knots, when the braid length does not come from a minimal stranded braid, a minimal stranded braid is given, as provided by [3].
Michael Gasser [4] has provided us with braid notation for all 13 crossing prime knots. These are not proved to be minimal. Their space orientations agree with their PD notation. They have not been tested for string orientation.
[1] Gittings, T., "Minimum Braids: A Complete Invariant of Knots and Links," Arxiv preprint.
[2] Jones, V. F. R., "Hecke algebra representations for braid groups and link polynomials," Ann. of Math., 126 (1987), 335-388.
[3] Stoimenow, A., Personal communication.
[3] Gasser, M., Personal communication.