  On a smooth domain in complex n space of finite D'Angelo q-type at a point,
an effective upper bound for the vanishing order of the Levi determinant
$\text{coeff}\{\partial r \wedge \dbar r \wedge (\partial \dbar r)^{n-q}\}$ at
that point is given in terms of the D'Angelo q-type, the dimension of the space
n, and q itself. The argument uses Catlin's notion of a boundary system as well
as techniques pioneered by John D'Angelo.
