A Boolean function f on n variables is said to be a bent function if the absolute value of all its Walsh coefficients is \(2^{n/2}\). Our main result is a new asymptotic lower bound on the number of Boolean bent functions. It is based on a modification of the Maiorana–McFarland family of bent functions and recent progress in the estimation of the number of transversals in latin squares and hypercubes. By-products of our proofs are the asymptotics of the logarithm of the numbers of partitions of the Boolean hypercube into 2-dimensional affine and linear subspaces.

中文翻译：

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弯曲函数数量的渐近下界

如果所有沃尔什系数的绝对值为\(2^{n/2}\) ，则n 个变量的布尔函数f被称为弯曲函数。我们的主要结果是布尔弯曲函数数量的新渐近下界。它基于 Maiorana–McFarland 弯曲函数族的修改以及最近在估计拉丁方和超立方体的横截数方面取得的进展。我们证明的副产品是布尔超立方体划分为二维仿射和线性子空间的数量的对数渐近。