Minor comment: the improvement over the state-of-the-art is in the second order term of the exponent. Their formula express det. with B_n = exp( n ln n - n lnl

Minor comment: the improvement over the state-of-the-art is in the second order term of the exponent. Their formula express det. with B_n = exp( n ln n - n lnln n - O(n)) terms. The old formula had exp(n ln n - O(n)) terms. It's a nice bound, but won't change much for non-theoretical results.