  It is shown in this paper that suitable weak solutions to the 6D steady
incompressible Navier-Stokes are H\"{o}lder continuous at $0$ provided that
$\int_{B_1}|u(x)|^3dx+\int_{B_1}|f(x)|^qdx$ or $\int_{B_1}|\nabla
u(x)|^2dx$+$\int_{B_1}|\nabla
u(x)|^2dx\left(\int_{B_1}|u(x)|dx\right)^2+\int_{B_1}|f(x)|^qdx$ with $q>3$ is
sufficiently small, which implies that the 2D Hausdorff measure of the set of
singular points is zero. For the boundary case, we obtain that $0$ is regular
provided that $\int_{B_1^+} |u(x)|^3 dx + \int_{B_1^+} |f(x)|^3 dx$ or
$\int_{B_1^+} |\nabla u(x)|^2 dx + \int_{B_1^+} |f(x)|^3 dx$ is sufficiently
small. These results improve previous regularity theorems by Dong-Strain
(\cite{DS}, Indiana Univ. Math. J., 2012), Dong-Gu (\cite{DG2}, J. Funct.
Anal., 2014), and Liu-Wang (\cite{LW}, J. Differential Equations, 2018), where
either the smallness of the pressure or the smallness on all balls is
necessary.
