  We present a new method for the reconstruction of rational functions through
finite-fields sampling that can significantly reduce the number of samples
required. The method works by exploiting all the independent linear relations
among target functions. Subsequently, the explicit solutions of the functions
can be efficiently obtained by solving the linear system. As a first
application, we utilize the method to address various examples within the
context of Feynman integrals reduction. These examples demonstrate that our
method can substantially improve the computational efficiency, making it useful
for future computations in particle physics.
