  In this paper we give a complete classification of totally-reflective,
primitive genera in dimension 3 and 4. Our method breaks up into two parts. The
first part consists of classifying the square free, totally-reflective,
primitive genera by calculating strong bounds on the prime factors of the
determinant of genera of positive definite quadratic forms (lattices) with this
property. We achieve these bounds by combining the Minkowski-Siegel mass
formula with the combinatorial classification of reflective lattices
accomplished by Scharlau \& Blaschke. In a second part, we use a lattice
transformation that goes back to Watson, to generate all totally-reflective,
primitive genera when starting with the square-free case.
