  In this paper, we are concerned with the upper box-counting dimension of the
set of possible singular points in space-time of suitable weak solutions to the
3D Navier-Stokes equations. By taking full advantage of the pressure $\Pi$ in
terms of $\nabla \Pi$ in equations, we show that this upper box dimension is at
most $135/104(\approx1.30)$, which improves the known upper box-counting
dimension $95/63(\approx1.51)$ in Koh et al. [9, J. Differential Equations,
261: 3137--3148, 2016], $45/29(\approx1.55)$ in Kukavica et al. [11,
Nonlinearity 25: 2775-2783, 2012] and $135/82(\approx1.65)$ in Kukavica [10,
Nonlinearity 22: 2889-2900, 2009].
