  In this paper, we present a deterministic algorithm to find a strong generic
position for an algebraic space curve. We modify our existing algorithm for
computing the topology of an algebraic space curve and analyze the bit
complexity of the algorithm. It is $\tilde{\mathcal {O}} (N^{20})$, where
$N=\max\{d,\tau\}$, $d, \tau$ are the degree bound and the bit size bound of
the coefficients of the defining polynomials of the algebraic space curve. To
our knowledge, this is the best bound among the existing work. It gains the
existing results at least $N^2$.
