  We use a quantum Monte Carlo method to calculate the Neel temperature T_N of
weakly coupled S=1/2 Heisenberg antiferromagnetic layers consisting of coupled
ladders. This system can be tuned to different two-dimensional scaling regimes
for T > T_N. In a single-layer mean-field theory,
\chi_s^{2D}(T_N)=(z_2J')^{-1}, where \chi_s^{2D} is the exact staggered
susceptibility of an isolated layer, J' the inter-layer coupling, and z_2=2 the
layer coordination number. With a renormalized z_2, we find that this
relationship applies not only in the renormalized-classical regime, as shown
previously, but also in the quantum-critical regime and part of the
quantum-disordered regime. The renormalization is nearly constant; k_2 ~
0.65-0.70. We also study other universal scaling functions.
