  The theta-block conjecture proposed by Gritsenko--Poor--Yuen in 2013
characterizes Siegel paramodular forms which are simultaneously Borcherds
products and additive Jacobi lifts. In this paper, we prove this conjecture for
two new infinite series of theta blocks of weights 2 and 3. The proof is based
on Scheithauer's classification of reflective modular forms of singular weight.
