  We study the problem of pointwise convegence for the Schr\"odinger operator
on $\mathbb R^n$ along time sequences. We show that the sharp counterexample to
the sequential Schr\"odinger maximal estimate given recently by Li, Wang and
Yan based in the construction by Luc\`a and Rogers can also be achieved with
the construction of Bourgain, and we extend it to the fractal setting.
