A mod-\(p\) transversal in a affine space over the field \(Z/2Z\) is a set whose intersection with any hyperplane which does not contain the origin contains a number of points not divisible by \(p\). The author provides an estimate on the minimal size \(f(p,n)\) of such a transversal in terms of the prime \(p\) and the dimension \(n\) of the affine space. The result as given by theorem 1 reads: \[ e^{-1}(p-1)^{(n/p-1)}-(p-1)\leq f(p,n)\leq(p-1)2^{\lceil(n/p-1)\rceil}-(p-1). \] The upper bound is proven by means of a simple direct construction. The lower bound is obtained by means of techniques involving the finite Fourier transform. It involves a so-called uncertainty inequality for finite Abelian groups which states that the for a nonzero function the product of the sizes of the supports for a function and its transform exceeds the order of the group. The problem is motivated by its usage in the theory of lower bounds for circuit complexity. More in particular the possibility and/or complexity of replacing unbounded fan in or gates by mod-\(n\) gates is discussed.