  APN functions play a fundamental role in cryptography against attacks on
block ciphers. Several families of quadratic APN functions have been proposed
in the recent years, whose construction relies on the existence of specific
families of polynomials. A key question connected with such constructions is to
determine whether such APN functions exist for infinitely many dimensions or
not.
  In this paper we consider a family of functions recently introduced by Li et
al. in 2021 showing that for any dimension $m\geq 3$ there exists an APN
function belonging to such a family.
  Our main result is proved by a combination of different techniques arising
from both algebraic varieties over finite fields connected with linearized
permutation rational functions and {partial vector space partitions}, together
with investigations on the kernels of linearized polynomials.
