# Lower bounds on APN-distance for all known APN functions

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The following tables list a lower bound on the Hamming distance between all known CCZ-inequivalent APN representatives up to dimension 11 using the methods described used in [1]. Note that the lower bound is a CCZ-invariant (unlike the exact minimum distance itself) and it can be calculated via the formula ${\displaystyle l(F)=\lceil {\frac {m_{F}}{3}}\rceil +1}$, where ${\displaystyle l(F)}$ is the lower bound on the Hamming distance between an ${\displaystyle (n,n)}$-function ${\displaystyle F}$ and the closest APN function, and ${\displaystyle m_{F}}$ is defined as ${\displaystyle m_{F}=\min _{b,\beta \in \mathbb {F} _{2^{n}}}|\{a\in \mathbb {F} _{2^{n}}:(\exists x\in \mathbb {F} _{2^{n}})(F(x)+F(a+x)+F(a+\beta )=b)\}|}$. The values of ${\displaystyle m_{F}}$ for the CCZ-inequivalent representatives are provided in the tables for convenience. The representatives for dimensions 7 and 8 are taken from the list ofKnown quadratic APN polynomial functions over GF(2^7) and Known quadratic APN polynomial functions over GF(2^8), respectively, while the rest are taken from the table of CCZ-inequivalent APN functions from the known APN classes over GF(2^n) (for n between 6 and 11).