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

BIQUANDLES OF SMALL SIZE AND SOME INVARIANTS OF VIRTUAL AND WELDED KNOTS