  We consider the question of which virtual knots have finite fundamental
medial bikei. We describe and implement an algorithm for completing a
presentation matrix of a medial bikei to an operation table, determining both
the cardinality and isomorphism class of the fundamental medial bikei, each of
which are link invariants. As an example, we compute the fundamental medial
bikei for all of the prime virtual knots with up to four classical crossings as
listed in the knot atlas.
