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Let $\mathbbF_2$ denote the binary field. A \emphBorellus generator of order $(n, m, r)$ is defined by:

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\subsectionBorell–TIS inequality For any $t>0$, [ \Pr\left( \sup_s \in S X_s > \mathbbE[\sup X_s] + t \right) \le e^-t^2/(2\sigma^2), ] where $\sigma^2$ is the maximal variance of $X_s$. This controls the deviation of the threshold function's output. Let $\mathbbF_2$ denote the binary field

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