Geodesic
Bounds for the number of Boolean functions admitting affine approximations of a~given accuracy
Diskretnaya Matematika, Tome 22 (2010) no. 4, pp. 3-19

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We obtain two-sided bounds and asymptotic formulas for the number of Boolean functions of $n$ variables which are approximated by affine or linear Boolean functions with a given accuracy. 
@article{DM_2010_22_4_a0,
     author = {A. M. Zubkov and A. A. Serov},
     title = {Bounds for the number of {Boolean} functions admitting affine approximations of a~given accuracy},
     journal = {Diskretnaya Matematika},
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     publisher = {mathdoc},
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     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2010_22_4_a0/}
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A. M. Zubkov; A. A. Serov. Bounds for the number of Boolean functions admitting affine approximations of a~given accuracy. Diskretnaya Matematika, Tome 22 (2010) no. 4, pp. 3-19. http://geodesic.mathdoc.fr/item/DM_2010_22_4_a0/