  The maximal minors of a matrix of indeterminates are a universal Gr\"obner
basis by a theorem of Bernstein, Sturmfels and Zelevinsky. On the other hand it
is known that they are not always a universal Sagbi basis. By an experimental
approach we discuss their behavior under varying monomial orders and their
extensions to Sagbi bases. These experiments motivated a new implementation of
the Sagbi algorithm which is organized in a Singular script and falls back on
Normaliz for the combinatorial computations. In comparison to packages in the
current standard distributions of Macaulay 2 and Singular it extends the range
of computability by at least one order of magnitude.
