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When a plain Monte Carlo estimate on $n$ samples has variance $\sigma^2/n$,then scrambled digital nets attain a variance that is $o(1/n)$ as $n\to\infty$.For finite $n$ and an adversarially selected integrand, the variance of ascrambled $(t,m,s)$-net can be at most $\Gamma\sigma^2/n$ for a maximal gaincoefficient $\Gamma<\infty$. The most widely used digital nets and sequencesare those of Sobol'. It was previously known that $\Gamma\leqslant 2^t3^s$ forSobol' points as well as Niederreiter-Xing points. In this paper we study netsin base $2$. We show that $\Gamma \leqslant2^{t+s-1}$ for nets. This bound is asimple, but apparently unnoticed, consequence of a microstructure analysis inNiederreiter and Pirsic (2001). We obtain a sharper bound that is smaller thanthis for some digital nets. We also show that all nonzero gain coefficientsmust be powers of two. A consequence of this latter fact is a simplifiedalgorithm for computing gain coefficients of nets in base $2$.

The nonzero gain coefficients of Sobol's sequences are always powers of two