Maximal sets of permutations constructed from projective planes

On the set of n²+n+1 points of a projective plane, a set of n²+n+1 permutations is constructed with the property that any two are a Hamming distance 2n+1 apart. Another set is constructed in which every pair are a Hamming distance not greater than 2n+1 apart. Both sets are maximal with respect to the stated property.