Using permutation rational functions to obtain permutation arrays with large hamming distance

We consider permutation rational functions ( PRFs ), V ( x )/ U ( x ), where both V ( x ) and U ( x ) are polynomials over a finite field F q . Permutation rational functions have been the subject of several recent papers. Let M ( n , D ) denote the maximum number of permutations on n symbols with pairwise Hamming distance D . Computing lower bounds for M ( n , D ) is the subject of current research with applications in error correcting codes. Using PRFs of specified degrees d we obtain improved lower bounds for M ( q , q - k ) for prime powers q and k ∈ { 5 , 6 , 7 , 8 , 9 } , and for M ( q + 1 , q - k ) for prime powers q and k ∈ { 4 , 5 , 6 , 7 , 8 , 9 } .