  An $n$-bit boolean function is resilient to coalitions of size $q$ if any
fixed set of $q$ bits is unlikely to influence the function when the other
$n-q$ bits are chosen uniformly. We give explicit constructions of depth-$3$
circuits that are resilient to coalitions of size $cn/\log^{2}n$ with bias
$n^{-c}$. Previous explicit constructions with the same resilience had constant
bias. Our construction is simpler and we generalize it to biased product
distributions.
  Our proof builds on previous work; the main differences are the use of a tail
bound for expander walks in combination with a refined analysis based on
Janson's inequality.
