On primitive elements of finite fields avoiding affine hyperplanes

Let n≥2 be an integer and let Fq the finite field with q elements, where is a prime power. Given Fq-affine hyperplanes A1,…,An of Fqn in general position, we study existence distribution primitive elements Fqn, avoiding each Ai. We obtain both asymptotic concrete results, relating to past works on digits over fields.