Aspects of this question have been thoroughly treated in The Classification of Finite Simple Groups, Number 3, by Gorenstein-Lyons-Solomon, AMS, 1994: see especially their Table 3.3.1 for the Chevalley groups. In your notation (which differs somewhat from theirs), the $p$-rank is $16a$. This gives only the rank of a maximal elementary abelian $p$-subgroup, however.
Jim Humphreys
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