A high-statistics measurement of the string tension $\sigma$ has been performed for SU(3) lattice gauge theory, paying particular attention to errors involved in the analysis, in the interval $\beta =\frac{6}{{g_0}^2}=4.8-7.0\mathrm{}$ on $6^4$, $8^4$, and ${10}^4$ lattices. A marked structure has been found in the string tension at $\beta =5.3-5.4\mathrm{}$. Beyond $\beta =5.5\mathrm{}$, our data are consistent with scaling with the ratio $\frac{{\Lambda }_L}{\sqrt{\sigma }}=(7.9\mathrm{}\pm 0.5)\times {10}^{-3\mathrm{}}$, a value larger than those previously reported. The approach to scaling is abrupt and from above, in contrast to the SU(2) case.

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