The limited time available for acquiring the channel state in mobile broadband wireless communication systems makes it crucial to count with channel estimation methods that attain the highest accuracy with a given preamble length. For the family of preambles that probe channels repeatedly at equispaced frequencies, we find that the shortest preamble that attains a given mean square error is a sequence that undersamples the channel spectrum, thereby allowing for a better mitigation of white Gaussian noise by averaging a higher number of observations.