  Using tools from algebraic geometry and Groebner basis theory we solve two
problems in network coding. First we present a method to determine the smallest
field size for which linear network coding is feasible. Second we derive
improved estimates on the success probability of random linear network coding.
These estimates take into account which monomials occur in the support of the
determinant of the product of Edmonds matrices. Therefore we finally
investigate which monomials can occur in the determinant of the Edmonds matrix.
