A note on the existence of sequences with small star discrepancy

It was shown by Heinrich et al. [The inverse of the star-discrepancy depends linearly on the dimension, Acta Arith. 96 (2001) 279–302] that there exist point sets for which the inverse of the star discrepancy depends linearly on the dimension. In this paper we extend those results by showing that there exist point sets extensible in the modulus and the dimension for which the star discrepancy satisfies a tractability bound for all dimensions and moduli.