Near-optimal time-space tradeoff for element distinctness

It was conjectured by A. Borodin et al. that to solve the element distinctness problem requires TS=Ω(n²) on a comparison-based branching program using space S and time T, which, if true, would be close to optimal since TS=O(n² log n) is achievable. They showed recently (1987) that TS=Ω(n^3/2(log n)^1/2 ). The author shows a near-optimal tradeoff TS=Ω( n^2-ε(n)), where ε(n)=O(1/(log n)^1/2)