We present an update on our determination of the light-quark connected contribution to the hadronic vacuum polarization (HVP) of the muon anomalous magnetic moment, $a_\mu$, on a finer lattice with 2+1+1 highly-improved staggered quark (HISQ) ensemble from the MILC collaboration with physical pion mass, 0.042 fm lattice spacing, and size $144^3 \times 288$ sites. Within the low-mode averaging (LMA) framework, the HVP correlator is decomposed into low-low (LL), high-low (HL), low-high (LH) and high-high (HH) components. Since the LL part dominates the total statistical uncertainty but is also the most computationally expensive to evaluate, we implement a sparsening strategy to construct the meson fields efficiently. This approach significantly reduces the computational cost while preserving signal quality. By combining the sparsened LL contribution with HL, LH and HH components, we achieve an improved determination of the light-quark connected HVP contribution to $a_\mu$.