<p>A lower bound to the number of AND gates used in parallel multipliers for <tmath>$GF(2/supm/)$</tmath>, under the condition that time complexity be minimum, is determined. In particular, the exact minimum number of AND gates for Primitive Normal Bases and Optimal Normal Bases of Type II multipliers is evaluated. This result indirectly suggests that space complexity is essentially a quadratic function of <tmath>$m$</tmath> when time complexity is kept minimum.</p>