In this paper we give the results of a computer search for biracks of small
size and we give various interpretations of these findings. The list includes
biquandles, racks and quandles together with new invariants of welded knots and
examples of welded knots which are shown to be non-trivial by the new
invariants. These can be used to answer various questions concerning virtual
and welded knots. As an application we reprove the result that the Burau map
from braids to matrices is non injective and give an example of a non-trivial
virtual (welded) knot which cannot be distinguished from the unknot by any
linear biquandles.