  Let G be a group. We say that G has spread r if for any set of distinct
elements {x1,..., xr}\subset G there exists an element y\in G with the property
that <xi, y>=G for every 0<i<r+1. Few bounds on the spread of finite simple
groups are known. In this paper we present improved upper bounds for the spread
of many of the sporadic simple groups, in some cases improving on the best
known upper bound by several orders of magnitude.
