# Sigma multiplicities for APN functions in dimensions up to 10

For all known APN functions over GF(2^n) with n up to 10, the following tables list the partitions of GF(2^n) induced by the multiplicities of the Sigma sets <math>\Sigma_F^k(0)</sigma> for k = 4, as explained in the SETA paper on testing EA-equivalences.

Due to the large number of functions, the results for dimension 8 are listed on a separate page.

## Dimension 9

## Dimension 10

Functions 1-10 are indexed according to [[1]]. The remaining functions correspond to the ones found via self-equivalences, and are indexed in the same way as in the provided dataset.

ID | Partition sizes |
---|---|

1 | 1, 341, 682 |

2 | 1, 341, 682 |

3 | 1, 341, 682 |

4 | 1, 341, 682 |

5 | 1, 341, 682 |

6 | 1, 341, 682 |

7 | 1, 341, 682 |

8 | 1, 341, 682 |

9 | 1, 341, 682 |

10 | 1, 341, 682 |

11 | 1, 341, 682 |

12 | 1, 341, 682 |

13 | 1, 341, 682 |

14 | 1, 341, 682 |

15 | 1, 341, 682 |

16 | 1, 341, 682 |

17 | 1, 31, 155, 155, 155, 217, 310 |

18 | 1, 341, 682 |

19 | 1, 124, 217, 310, 372 |

20 | 1, 341, 682 |

21 | 1, 11, 11, 165, 330, 506 |