  Let $A$ and $B$ be disjoint sets of sizes $a$ and $b$, respectively. Let
$f(a,b)$ denote the minimum number of quadruples needed to cover all triples $T
\subseteq A \cup B$ such that $|T \cap A| \geq 2$. We prove upper and lower
bounds on $f(a,b)$ and use them to derive upper bounds for the
$(n,4,3,4)$-lottery problem.
