[On _Azimuth_](https://johncarlosbaez.wordpress.com/2016/05/06/shelves-and-the-infinite/#comment-79817), on May 6, 2016, [Joseph van Name](http://mathoverflow.net/users/22277/joseph-van-name) wrote:

> The largest classical Laver table computed is actually $A_{48}$. The 48th table was computed by Dougherty and the algorithm was originally described in Dougherty's paper [here](http://arxiv.org/abs/math/9503204). With today's technology I could imagine that one could compute $A_{96}$ if one has access to a sufficiently powerful computer.  

> One can compute the classical Laver tables up to the 48th table on your computer [here](http://boolesrings.org/jvanname/lavertables-computation-classical-tablecalculator/) at my website.