  We consider the problem of allocating indivisible goods to agents with
additive valuation functions. Kurokawa, Procaccia and Wang [JACM, 2018] present
instances for which every allocation gives some agent less than her maximin
share. We present such examples with larger gaps. For three agents and nine
items, we design an instance in which at least one agent does not get more than
a $\frac{39}{40}$ fraction of her maximin share. Moreover, we show that there
is no negative example in which the difference between the number of items and
the number of agents is smaller than six, and that the gap (of $\frac{1}{40}$)
of our example is worst possible among all instances with nine items.
  For $n \ge 4$ agents, we show examples in which at least one agent does not
get more than a $1 - \frac{1}{n^4}$ fraction of her maximin share. In the
instances designed by Kurokawa, Procaccia and Wang, the gap is exponentially
small in $n$.
