Permutation group acting on a set of cardinality 8
Order = 6 = 2 * 3
(1, 6, 3, 8, 5, 7)(2, 4)
(1, 8)(2, 4)(3, 7)(5, 6)
Number of bent functions: 8
Bent functions (of degree 3):
[
x1*x2*x3 + x1*x2*x5 + x1*x2*x7 + x1*x2*x8 + x1*x3*x8 + x1*x4*x6 + x1*x4*x8 +
x1*x5*x6 + x1*x7*x8 + x2*x3*x5 + x2*x3*x6 + x2*x3*x7 + x2*x5*x6 +
x2*x5*x8 + x3*x4*x7 + x3*x4*x8 + x3*x5*x7 + x3*x6*x7 + x4*x5*x6 +
x4*x5*x7 + x4*x6*x7 + x4*x6*x8 + x4*x7*x8 + x5*x6*x8,
x1*x2*x6 + x1*x2*x8 + x1*x3*x4 + x1*x3*x8 + x1*x4*x5 + x1*x4*x7 + x1*x4*x8 +
x1*x5*x6 + x1*x7*x8 + x2*x3*x7 + x2*x3*x8 + x2*x5*x6 + x2*x5*x7 +
x2*x6*x7 + x2*x6*x8 + x2*x7*x8 + x3*x4*x5 + x3*x4*x6 + x3*x4*x7 +
x3*x5*x7 + x3*x6*x7 + x4*x5*x6 + x4*x5*x8 + x5*x6*x8,
x1*x2*x3 + x1*x2*x5 + x1*x2*x6 + x1*x2*x8 + x1*x3*x5 + x1*x3*x6 + x1*x3*x7 +
x1*x4*x7 + x1*x4*x8 + x1*x5*x7 + x1*x5*x8 + x1*x6*x7 + x1*x6*x8 +
x2*x3*x5 + x2*x3*x7 + x2*x3*x8 + x2*x5*x6 + x2*x5*x7 + x3*x4*x6 +
x3*x4*x7 + x3*x5*x6 + x3*x5*x8 + x3*x6*x8 + x3*x7*x8 + x4*x5*x6 +
x4*x5*x8 + x4*x6*x7 + x4*x6*x8 + x4*x7*x8 + x5*x6*x7 + x5*x7*x8 +
x6*x7*x8,
x1*x2*x3 + x1*x2*x5 + x1*x2*x6 + x1*x2*x8 + x1*x3*x7 + x1*x4*x7 + x1*x4*x8 +
x1*x5*x8 + x1*x6*x8 + x2*x3*x5 + x2*x3*x7 + x2*x3*x8 + x2*x5*x6 +
x2*x5*x7 + x3*x4*x6 + x3*x4*x7 + x3*x5*x6 + x3*x7*x8 + x4*x5*x6 +
x4*x5*x8 + x4*x6*x7 + x4*x6*x8 + x4*x7*x8 + x5*x6*x7,
x1*x2*x7 + x1*x2*x8 + x1*x3*x4 + x1*x3*x7 + x1*x4*x5 + x1*x4*x6 + x1*x4*x8 +
x1*x5*x8 + x1*x6*x8 + x2*x3*x6 + x2*x3*x7 + x2*x5*x6 + x2*x5*x8 +
x2*x6*x7 + x2*x6*x8 + x2*x7*x8 + x3*x4*x5 + x3*x4*x7 + x3*x4*x8 +
x3*x5*x6 + x3*x7*x8 + x4*x5*x6 + x4*x5*x7 + x5*x6*x7,
x1*x2*x7 + x1*x2*x8 + x1*x3*x4 + x1*x3*x5 + x1*x3*x6 + x1*x3*x7 + x1*x4*x5 +
x1*x4*x6 + x1*x4*x8 + x1*x5*x7 + x1*x5*x8 + x1*x6*x7 + x1*x6*x8 +
x2*x3*x6 + x2*x3*x7 + x2*x5*x6 + x2*x5*x8 + x2*x6*x7 + x2*x6*x8 +
x2*x7*x8 + x3*x4*x5 + x3*x4*x7 + x3*x4*x8 + x3*x5*x6 + x3*x5*x8 +
x3*x6*x8 + x3*x7*x8 + x4*x5*x6 + x4*x5*x7 + x5*x6*x7 + x5*x7*x8 +
x6*x7*x8,
x1*x2*x6 + x1*x2*x8 + x1*x3*x4 + x1*x3*x5 + x1*x3*x6 + x1*x3*x8 + x1*x4*x5 +
x1*x4*x7 + x1*x4*x8 + x1*x5*x6 + x1*x5*x7 + x1*x6*x7 + x1*x7*x8 +
x2*x3*x7 + x2*x3*x8 + x2*x5*x6 + x2*x5*x7 + x2*x6*x7 + x2*x6*x8 +
x2*x7*x8 + x3*x4*x5 + x3*x4*x6 + x3*x4*x7 + x3*x5*x7 + x3*x5*x8 +
x3*x6*x7 + x3*x6*x8 + x4*x5*x6 + x4*x5*x8 + x5*x6*x8 + x5*x7*x8 +
x6*x7*x8,
x1*x2*x3 + x1*x2*x5 + x1*x2*x7 + x1*x2*x8 + x1*x3*x5 + x1*x3*x6 + x1*x3*x8 +
x1*x4*x6 + x1*x4*x8 + x1*x5*x6 + x1*x5*x7 + x1*x6*x7 + x1*x7*x8 +
x2*x3*x5 + x2*x3*x6 + x2*x3*x7 + x2*x5*x6 + x2*x5*x8 + x3*x4*x7 +
x3*x4*x8 + x3*x5*x7 + x3*x5*x8 + x3*x6*x7 + x3*x6*x8 + x4*x5*x6 +
x4*x5*x7 + x4*x6*x7 + x4*x6*x8 + x4*x7*x8 + x5*x6*x8 + x5*x7*x8 +
x6*x7*x8
]
Permutation group acting on a set of cardinality 8
Order = 7
(1, 3, 7, 8, 6, 4, 2)
Number of bent functions: 12
Bent functions (of degree 3):
[
x1*x2*x3 + x1*x2*x4 + x1*x2*x6 + x1*x2*x8 + x1*x3*x4 + x1*x3*x6 + x1*x3*x7 +
x1*x5*x6 + x1*x5*x8 + x1*x6*x8 + x1*x7*x8 + x2*x3*x7 + x2*x4*x6 +
x2*x4*x7 + x2*x4*x8 + x2*x5*x7 + x2*x5*x8 + x2*x7*x8 + x3*x4*x5 +
x3*x4*x6 + x3*x4*x7 + x3*x5*x6 + x3*x6*x8 + x3*x7*x8 + x4*x5*x7 +
x4*x6*x7 + x4*x6*x8 + x6*x7*x8,
x1*x2*x3 + x1*x2*x4 + x1*x2*x7 + x1*x2*x8 + x1*x3*x6 + x1*x3*x7 + x1*x3*x8 +
x1*x4*x5 + x1*x4*x6 + x1*x4*x7 + x1*x4*x8 + x1*x5*x7 + x1*x6*x7 +
x1*x6*x8 + x2*x3*x4 + x2*x3*x5 + x2*x3*x6 + x2*x3*x8 + x2*x4*x6 +
x2*x4*x7 + x2*x5*x6 + x2*x6*x7 + x2*x6*x8 + x2*x7*x8 + x3*x4*x6 +
x3*x4*x7 + x3*x4*x8 + x3*x5*x8 + x3*x6*x7 + x3*x7*x8 + x4*x5*x8 +
x4*x6*x8 + x4*x7*x8 + x5*x6*x7 + x6*x7*x8,
x1*x2*x6 + x1*x2*x8 + x1*x3*x4 + x1*x3*x6 + x1*x4*x5 + x1*x4*x7 + x1*x4*x8 +
x1*x5*x7 + x1*x6*x7 + x1*x6*x8 + x1*x7*x8 + x2*x3*x5 + x2*x3*x6 +
x2*x3*x7 + x2*x3*x8 + x2*x4*x7 + x2*x4*x8 + x2*x5*x6 + x2*x6*x7 +
x2*x7*x8 + x3*x4*x6 + x3*x4*x7 + x3*x4*x8 + x3*x5*x8 + x3*x6*x8 +
x4*x5*x8 + x4*x6*x7 + x5*x6*x7,
x1*x2*x3 + x1*x2*x4 + x1*x2*x5 + x1*x2*x7 + x1*x2*x8 + x1*x3*x5 + x1*x3*x6 +
x1*x3*x7 + x1*x3*x8 + x1*x4*x6 + x1*x4*x7 + x1*x4*x8 + x1*x6*x7 +
x1*x6*x8 + x2*x3*x4 + x2*x3*x6 + x2*x3*x8 + x2*x4*x5 + x2*x4*x6 +
x2*x4*x7 + x2*x6*x7 + x2*x6*x8 + x2*x7*x8 + x3*x4*x6 + x3*x4*x7 +
x3*x4*x8 + x3*x5*x7 + x3*x6*x7 + x3*x7*x8 + x4*x5*x6 + x4*x6*x8 +
x4*x7*x8 + x5*x6*x8 + x5*x7*x8 + x6*x7*x8,
x1*x2*x7 + x1*x2*x8 + x1*x3*x6 + x1*x3*x8 + x1*x4*x5 + x1*x4*x6 + x1*x4*x7 +
x1*x4*x8 + x1*x5*x7 + x1*x6*x7 + x1*x6*x8 + x2*x3*x4 + x2*x3*x5 +
x2*x3*x6 + x2*x3*x8 + x2*x4*x7 + x2*x5*x6 + x2*x6*x7 + x2*x6*x8 +
x2*x7*x8 + x3*x4*x6 + x3*x4*x7 + x3*x4*x8 + x3*x5*x8 + x3*x6*x7 +
x4*x5*x8 + x4*x7*x8 + x5*x6*x7,
x1*x2*x3 + x1*x2*x4 + x1*x2*x5 + x1*x2*x6 + x1*x2*x8 + x1*x3*x4 + x1*x3*x5 +
x1*x3*x6 + x1*x3*x7 + x1*x4*x7 + x1*x4*x8 + x1*x6*x7 + x1*x6*x8 +
x1*x7*x8 + x2*x3*x6 + x2*x3*x7 + x2*x3*x8 + x2*x4*x5 + x2*x4*x6 +
x2*x4*x7 + x2*x4*x8 + x2*x6*x7 + x2*x7*x8 + x3*x4*x6 + x3*x4*x7 +
x3*x4*x8 + x3*x5*x7 + x3*x6*x8 + x3*x7*x8 + x4*x5*x6 + x4*x6*x7 +
x4*x6*x8 + x5*x6*x8 + x5*x7*x8 + x6*x7*x8,
x1*x2*x3 + x1*x2*x4 + x1*x2*x7 + x1*x2*x8 + x1*x3*x6 + x1*x3*x7 + x1*x3*x8 +
x1*x4*x6 + x1*x5*x6 + x1*x5*x8 + x1*x6*x8 + x2*x3*x4 + x2*x4*x6 +
x2*x4*x7 + x2*x5*x7 + x2*x5*x8 + x2*x6*x8 + x2*x7*x8 + x3*x4*x5 +
x3*x4*x6 + x3*x4*x7 + x3*x5*x6 + x3*x6*x7 + x3*x7*x8 + x4*x5*x7 +
x4*x6*x8 + x4*x7*x8 + x6*x7*x8,
x1*x2*x3 + x1*x2*x4 + x1*x2*x7 + x1*x2*x8 + x1*x3*x6 + x1*x3*x7 + x1*x3*x8 +
x1*x4*x6 + x1*x4*x7 + x1*x4*x8 + x1*x5*x6 + x1*x5*x8 + x1*x6*x7 +
x1*x6*x8 + x2*x3*x4 + x2*x3*x6 + x2*x3*x8 + x2*x4*x6 + x2*x4*x7 +
x2*x5*x7 + x2*x5*x8 + x2*x6*x7 + x2*x6*x8 + x2*x7*x8 + x3*x4*x5 +
x3*x4*x6 + x3*x4*x7 + x3*x4*x8 + x3*x5*x6 + x3*x6*x7 + x3*x7*x8 +
x4*x5*x7 + x4*x6*x8 + x4*x7*x8 + x6*x7*x8,
x1*x2*x3 + x1*x2*x4 + x1*x2*x6 + x1*x2*x8 + x1*x3*x4 + x1*x3*x6 + x1*x3*x7 +
x1*x4*x7 + x1*x4*x8 + x1*x5*x6 + x1*x5*x8 + x1*x6*x7 + x1*x6*x8 +
x1*x7*x8 + x2*x3*x6 + x2*x3*x7 + x2*x3*x8 + x2*x4*x6 + x2*x4*x7 +
x2*x4*x8 + x2*x5*x7 + x2*x5*x8 + x2*x6*x7 + x2*x7*x8 + x3*x4*x5 +
x3*x4*x6 + x3*x4*x7 + x3*x4*x8 + x3*x5*x6 + x3*x6*x8 + x3*x7*x8 +
x4*x5*x7 + x4*x6*x7 + x4*x6*x8 + x6*x7*x8,
x1*x2*x3 + x1*x2*x4 + x1*x2*x5 + x1*x2*x6 + x1*x3*x4 + x1*x3*x5 + x1*x3*x7 +
x1*x4*x7 + x1*x4*x8 + x1*x6*x7 + x1*x7*x8 + x2*x3*x6 + x2*x3*x7 +
x2*x3*x8 + x2*x4*x5 + x2*x4*x6 + x2*x4*x8 + x2*x6*x7 + x3*x4*x8 +
x3*x5*x7 + x3*x6*x8 + x3*x7*x8 + x4*x5*x6 + x4*x6*x7 + x4*x6*x8 +
x5*x6*x8 + x5*x7*x8 + x6*x7*x8,
x1*x2*x3 + x1*x2*x4 + x1*x2*x5 + x1*x2*x7 + x1*x3*x5 + x1*x3*x7 + x1*x3*x8 +
x1*x4*x6 + x1*x4*x7 + x1*x4*x8 + x1*x6*x7 + x2*x3*x4 + x2*x3*x6 +
x2*x3*x8 + x2*x4*x5 + x2*x4*x6 + x2*x6*x7 + x2*x6*x8 + x3*x4*x8 +
x3*x5*x7 + x3*x6*x7 + x3*x7*x8 + x4*x5*x6 + x4*x6*x8 + x4*x7*x8 +
x5*x6*x8 + x5*x7*x8 + x6*x7*x8,
x1*x2*x3 + x1*x2*x4 + x1*x2*x6 + x1*x2*x8 + x1*x3*x4 + x1*x3*x6 + x1*x3*x7 +
x1*x4*x5 + x1*x4*x7 + x1*x4*x8 + x1*x5*x7 + x1*x6*x7 + x1*x6*x8 +
x1*x7*x8 + x2*x3*x5 + x2*x3*x6 + x2*x3*x7 + x2*x3*x8 + x2*x4*x6 +
x2*x4*x7 + x2*x4*x8 + x2*x5*x6 + x2*x6*x7 + x2*x7*x8 + x3*x4*x6 +
x3*x4*x7 + x3*x4*x8 + x3*x5*x8 + x3*x6*x8 + x3*x7*x8 + x4*x5*x8 +
x4*x6*x7 + x4*x6*x8 + x5*x6*x7 + x6*x7*x8
]