  Explosive percolation (EP) has received significant research attention due to
its rich and anomalous phenomena near criticality. In our recent study [Phys.
Rev. Lett. 130, 147101 (2023)], we demonstrated that the correct critical
behaviors of the EP in infinite dimensions (complete graph) can be accurately
extracted using the event-based method, with finite-size scaling behaviors
still described by the standard finite-size scaling theory. We perform an
extensive simulation of the EPs on hypercubic lattices ranging from dimensions
$d=2$ to $6$, and find that the critical behaviors consistently obey the
standard finite-size scaling theory. Consequently, we obtain a high-precision
determination of the percolation thresholds and critical exponents, revealing
that the EPs governed by the product and sum rules belong to different
universality classes. Remarkably, despite the mean of the dynamic
pseudo-critical point $\mathcal{T}_L$ deviating from the infinite-lattice
criticality by a distance determined by the $d$-dependent correlation-length
exponent, $\mathcal{T}_L$ follows a normal (Gaussian) distribution across all
dimensions, with a standard deviation proportional to $1/\sqrt{V}$, where $V$
denotes the system volume. A theoretical argument associated with the
central-limit theorem is further proposed to understand the probability
distribution of $\mathcal{T}_L$. These findings offer a comprehensive
understanding of critical behaviors in EPs across various dimensions.
