Base sizes for simple groups and a conjecture of Cameron

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On base sizes for actions of finite classical groups (2007, background): “The main theorem of [3] states that the Liebeck–Shalev result holds with an explicit constant ≈ 1/2.”
Base sizes for sporadic simple groups (2010, background): “Base sizes for almost simple primitive permutation groups have been much studied in recent years (see [8, 10, 11, 18, 19, 20], for example).”
On base sizes for symmetric groups (2011, background): “In [4, 5], it is proved that b(G) 6 for any almost simple primitive group G of Lie type (excluding subspace actions of classical groups, of course).”
Base size, metric dimension and other invariants of groups and graphs (2011, background): “Progress towards this conjecture has been made by Gluck and various coauthors [59, 60], by Liebeck and Shalev [76], and in the (unpublished) PhD thesis of Benbenishty [13]; see [77] for further details.”