On Macula's error-correcting pool designs

Abstract

We show that Macula's claim of a Hamming distance 4 between any two candidate sets of positive clones in his pool design is incorrect. However, a previous proof of his on a weaker result (with a condition on design parameters) is correct. We also show that the condition is sharp and the distance 4 result is also sharp for arbitrary parameter values. (C) 2003 Elsevier Science B.V. All rights reserved.