An explicit upper bound for the Helfgott delta in SL(2,p)

Helfgott proved that there exists a $δ>0$ such that if $S$ is a symmetric generating subset of $SL(2,p)$ containing 1 then either $S^3=SL(2,p)$ or $|S^3|\geq |S|^{1+δ}$. It is known that $δ\geq 1/3024$. Here we show that $δ\leq(\log_2(7)-1)/6 \approx 0.3012$ and we present evidence suggesting that this might be the true value of $δ$.

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