The freeness of hyperplane arrangements in a three dimensional vector space over finite field is discussed. We prove that if the number of hyperplanes is greater than some bound, then the freeness is determined by the characteristic polynomial.
Masahiko Yoshinaga. "Free arrangements over finite field." Proc. Japan Acad. Ser. A Math. Sci. 82 (10) 179 - 182, JANUARY 2007. https://doi.org/10.3792/pjaa.82.179