We give a function h:01n01 such that every deMorgan formula of size n3−o(1)r2 agrees with h on at most a fraction of 21+2−(r) of the inputs. This improves the previous average-case lower bound of Komargodski and Raz (STOC, 2013).

Our technical contributions include a theorem that shows that the ``expected shrinkage'' result of Håstad (SIAM J. Comput., 1998) actually holds with very high probability (where the restrictions are chosen from a certain distribution that takes into account the structure of the formula), combining ideas of both Impagliazzo, Meka and Zuckerman (FOCS, 2012) and Komargodski and Raz. In addition, using a bit-fixing extractor in the construction of h allows us to simplify a major part of the analysis of Komargodski and Raz