A note on cover-free families

Abstract

Let N((r,w,d),t) denote the minimum number of points in a (r, w; d)-cover-free family having t blocks. Hajiabolhassan and Moazami (2012) [6] showed that the Hadamard conjecture is equivalent to confirm N((l, l;d),4d - 1) = Ad - 1. Hence, it is a challenging and interesting problem to determine the exact value of N((r,w;d),t). In this paper, we determine the exact value of N((r,w,d),t) for every r, w, where r + w≤t and some d. © 2018 Utilitas Mathematica Publishing Inc. All rights reserved.