Abstract
We show that the minimal base size b(G) of a finite primitive permutation group G of degree n is at most 2(log|G|/logn)+24. This bound is asymptotically best possible since there exists a sequence of primitive permutation groups G of degrees n such that b(G)=⌊2(log|G|/logn)⌉−2 and b(G) is unbounded. As a corollary we show that a primitive permutation group of degree n that does not contain the alternating group Alt(n) has a base of size at most max{n,25}.
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