A permuted van der Corput sequence \( S_b^\sigma \) in base \( b \) is a one-dimensional, infinite sequence of real numbers in the interval \( [0,1) \), generation of which involves a permutation \( \sigma \) of the set \( \{0, 1, \ldots, b-1\} \). These sequences are known to have low discrepancy \( D_N \), i.e. \( t(S_b^\sigma) := \limsup_{N \to \infty} D_N(S_b^\sigma) / \log N \) is finite. Restricting to prime bases \( p \) we present two families of generating permutations. We describe their elements as polynomials over finite fields \( \mathbb{F}_p \) in an explicit way. We use this characterization to obtain bounds for \( t(S_p^\sigma) \) for permutations \( \sigma \) in these families. We determine the best permutations in our first family and show that all permutations of the second family improve the distribution behavior of classical van der Corput sequences in the sense that \( t(S_p^\sigma) < t(S_p^{\mathrm{id}}) \).