van Rees Loops

With Michael Kinyon I wrote a paper investigating latin squares with the maximum possible number of 3x3 subsquares. van Rees showed that you can never have more than n2(n-1)/18 subsquares of order 3 in a latin square of order n. Moreover, he conjectured that this bound is achievable only when n is a power of 3.

In our paper we found a number of algebraically interesting loops/quasigroups whose Cayley tables achieve the van Rees bound. Here they are:

Back to main data homepage.