A new lower bound on the t-parameter of (t, s)-sequences

Let t(b) (s) denote the least t such that a (t, s)-sequence in base b exists. We present a new lower bound on t(b)(s), namely t(b)(s) > 1/b-1s-1/b-1-1/log b-log(b)(1+s(1-1/b+log(b)s)log b), which leads to the new asymptotic result L-b* := lim(s ->infinity) inf t(b)(s)/s >= 1/b-1. The best previously known result has been L-b* >= 1/b for arbitrary b >= 2 and L-2* >= log(2) 3-1.