  The problem of classifying tuples of nilpotent matrices over a field under
simultaneous conjugation is considered "hopeless". However, for any given
matrix order over a finite field, the number of concerned orbits is always
finite. This paper gives a closed formula for the number of absolutely
indecomposable orbits using the same methodology as Hua [5]; those orbits are
non-splittable over field extensions. As a consequence, those numbers are
always polynomials in the cardinality of the base field with integral
coefficients. It is conjectured that those coefficients are always
non-negative.
