Non-Isomorphic Minimal Bicovers of \(K_8\)

Abstract

The number \(g^{(4)}_{2}\) is the minimal number of blocks that contain all pairs from a set of \(8\) elements exactly twice under the restriction that the longest block has size \(4\) (this longest block need not be unique). Thus the blocks have lengths \(2, 3\), and \(4\). We show that there are three solutions to this problem.