Mehdi Azadi Motlagh

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((1; 1; d); 4d − 1) = 4d − 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.