Upper bounds on the uniform spreads of the sporadic simple groups

‎‎a finite group g has uniform spread k if there exists a fixed conjugacy class c of elements in g with the property that‎ ‎for any k nontrivial elements s1,s2,‎…‎,sk in g there exists y∈c such that g=(si,y) for i=1,2,‎…,k‎. ‎further‎, ‎the exact uniform spread of g is the largest k such that g has the uniform spread k‎. ‎in this paper we give upper bounds on the exact uniform spreads of thirteen sporadic simple groups‎.