Good permutations for extreme discrepancy

AbstractThe asymptotic behaviour of the discrepancy of the usual van der Corput sequences in arbitrary base b is known; and the implied constants tend to infinity with the base b. The aim of this paper is, first, to prove that for every base b there exist permutations of the digits such that the constants are less than 1Log 2 = 1.442… and, second, to produce a permutation, in base b = 36, giving the smallest discrepancy presently known: lim sup(D(N)Log N) = 23(35 Log 6) = 0.366…