## Known instances of APN functions over \( \mathbb{F}_{2^n} \)

- Known APN Power Functions \(x^d\) over \( \mathbb{F}_{2^n}\)
- List of known quadratic APN Polynomials
- Known switching classes of APN functions in \( \mathbb{F}_{2^5} \)
- Known switching classes of APN functions in \( \mathbb{F}_{2^6} \)
- Known switching classes of APN functions in \( \mathbb{F}_{2^7} \)
- Known switching classes of APN functions in \( \mathbb{F}_{2^8} \)
- CCZ-inequivalent representatives from the known infinite families over \(\mathbb{F}_{2^n}\) for \(6 \le n \le 11\)
- Classification of Quadratic APN Trinomials, Quadrinomials, Pentanomials, Hexanomials (CCZ-inequivalent with infinite monomial families) in Small Dimensions with all Coefficients equal to \(1\)
- New APN polynomials (up to CCZ-equivalence) over \( \mathbb{F}_{2^{11}}\)

## Known instances of generalized bent functions over \( \mathbb{F}_{p^n} \)

## Properties of certain APN functions over \( \mathbb{F}_{2^n} \)

- Power APN Permutations and their Inverses for Odd Dimensions \(3 \leqslant n \leqslant 129\)
- APN power functions, \( x^d \) , over the field \( \mathbb{F}_{2^n} \)
- Maximum number of solutions to \( f(x + a) + f(x) = b \) for power functions, \( x^d \) , over the field \( \mathbb{F}_{2^n} \), for \( n = 2, \ldots, 6 \)
- The Walsh Spectra of some Functions (under the assumption \(F(0) = 0\))

## Currently known optimal values for APN functions over \( \mathbb{F}_{2^n} \)

- Known Optimal Values and Classes for Differential Uniformity and Nonlinearity from \( \mathbb{F}_{2^n}\) to \( \mathbb{F}_{2^m}\)
- Known power permutations \(x^d\) with the highest known nonlinearity over \( \mathbb{F}_{2^n}\), \(n = 2t\)
- Highest Algebraic Degree of the Known APN Functions over \( \mathbb{F}_{2^n}\)