S-box and Side Channel Attacks
I think you have mis-understanding and misconception of how nonlinearity of sbox influences on side channel.

The 112 is nonlinear value of good properties sbox (such as AES) , I have not seen sbox with greater value in my literature.

I will go beyond you question, to evaluate s-box against side channel attack such as differential power analysis (DPA), other parameters are taken : Transparency order (TO) (the lower the TO, provides higher resistance to DPA) and signal to noise ratio (SNR) ( the lower the SNR ,provides  higher resistance to DPA).  

Prouff showed in his paper (DPA Attacks and S-Boxes), the highly nonlinear s-box are prone to DPA and   the construction of highly-nonlinear S-boxes with small transparency order (close to 0) is an open problem. 

I recommend you download the SET tool from this link and start to play it with different constructions of Sbox to gain more knowledge