accuracy one reaches depends highly on the system size reached in the calculation. $^{For the 3-12 lattice and the (1}$×$^{1) : (1}$×$^{1) (the kagome) and (2}$×$^{2) : (2}$×2) kagome-type subnet lattices, the largest dimension of the arrays used to store the values and the positions of nonzero elements of the sparse matrices is d ( m ) L $_{+1}$. The largest system size we reached is L = 15 with d ( m ) 16 = 335897865. For the (3 × $^{3) : (3}$× 3) and (4 × 4) : (4 × 4) kagome-type subnet lattices, the sparse matrix T$_{2}$ in the magnetic sector is further decomposed in two rectangular matrices of dimensions d ( m ) L +1 × d ( m ) L +2 and d ( m ) L +2 × d ( m ) L $_{+1}$, and the largest system size we reached is L = 14. The computer memory requirement for the calculations of the largest system is about 65 gigabytes, which is quite large, but the CPU time consumed is rather modest. It is just a few hours for a typical calculation of the magnetic scaled gap. The magnetic scaling dimension X$_{h}$ is estimated by extrapolating the scaled gaps X$_{h}$ ( v$_{c}$ ( L ) , L ) at the solution of (25) for a sequence of increasing system sizes in accordance with (27). The free energy density at the estimated critical point is calculated using (28) and the conformal anomaly c is computed by making use of the finite-size scaling relation (29). Details of the data fitting procedure are described in [16]. We also checked corrections to scaling due to the leading irrelevant field. Take the simple kagome lattice as an example. According to the Coulomb gas theory [29], y$_{t}$$_{2}$ $^{= 4}$− 4 /g with g given in (31) is the second leading thermal exponent, which we expect to be a candidate for the leading correction exponent y$_{u}$ . For q > 2, we indeed found y$_{u}$ close to y$_{t}$$_{2}$ . For q = 0 . 5, y$_{u}$ is about − 2 . 00(1), which is the analytic one. For q = 1 . 0 and 1.5, we found y$_{u}$ = − 1 . 79(3) and − 1 . 51(2) respec- tively, which dominate and overcome the corresponding y$_{t}$$_{2}$ . For q = 2, the Ising model, we obtain y$_{u}$ = − 4 . 00(1). The amplitudes of y$_{t}$$_{2}$ = − 4 / 3 and the analytic y$_{u}$ = − 2 corrections vanish. This is understandable for lattices with sixfold rotational symmetry. This picture is generally true for all ( $^{n}$× n ) : ( $^{n}$× n ) kagome subnet lattices. We summarize in Tables I-V numerical results of our calculations on the critical point v$_{c}$ , conformal anomaly c , and magnetic scaling dimension X$_{h}$ together with the universality predictions of c and X$_{h}$ . We have also computed v$_{c}$ using the homogeneity assumption and list the results. The v$_{c}$ calculation for the kagome lattice extends those of [30] using Monte Carlo renormalization group method and finite-site scaling analysis for q = 1 , 2 , 3 , 4 . Our study extends to non-integer q and offers results with higher accuracy. For q = 2, the Ising model, our numerical estimates of the critical threshold agree with the exact critical results up to 7 or 8 decimal numbers. This probably indicates the limit 15