On the Bipacking Numbers $g_2^{(4)}(\nu )$

Abstract

The quantity $g_2^{(k)}(v)$ is the minimum number of blocks in a family of blocks from a $v$-set that covers all $(\genfrac{}{}{0ex}{}{v}{2})$ pairs exactly twice, given the restriction that the longest block in the covering family has length $k$ (there may be many blocks of length $k$). We give certain results for the case $k=4$.