Title: On absolutely normal numbers and their discrepancy estimate,
Abstract: We construct the base $2$ expansion of an absolutely normal real number $x$
so that, for every integer $b$ greater than or equal to $2$, the discrepancy
modulo $1$ of the sequence $(b^0 x, b^1 x, b^2 x , \ldots)$ is essentially the
same as that realized by almost all real numbers.