Non-Isomorphic Minimal Bicovers of $K_8$

Abstract

The number $g_2^{(4)}$ 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.