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

Helfgott proved that there exists a δ>0δ>0 such that if S   is a symmetric generating subset of SL(2,p)SL(2,p) containing 1 then either S3=SL(2,p)S3=SL(2,p) or |S3|≥|S|1+δ|S3|≥|S|1+δ. It is known that δ≥1/3024δ≥1/3024. Here we show that δ≤(log2⁡(7)−1)/6≈0.3012δ≤(log2⁡(7)−1)/6≈0.3012 and we present evidence suggesting that this might be the true value of δ.