  We study randomized quasi-Monte Carlo integration by scrambled nets. The
scrambled net quadrature has long gained its popularity because it is an
unbiased estimator of the true integral, allows for a practical error
estimation, achieves a high order decay of the variance for smooth functions,
and works even for $L^p$-functions with any $p\geq 1$. The variance of the
scrambled net quadrature for $L^2$-functions can be evaluated through the set
of the so-called gain coefficients.
  In this paper, based on the system of Walsh functions and the concept of dual
nets, we provide improved upper bounds on the gain coefficients for digital
nets in general prime power base. Our results explain the known bound by Owen
(1997) for Faure sequences, the recently improved bound by Pan and Owen (2021)
for digital nets in base 2 (including Sobol' sequences as a special case), and
their finding that all the nonzero gain coefficients for digital nets in base 2
must be powers of two, all in a unified way.
