Hi folks,

As some may know already, I'm about to complete my thesis on the enumeration of Latin rectangles.

Here's a link discussing some of my work.

Currently I'm thinking about future projects after I submit (in a few weeks). One such idea is extending the tables of R(k,n) (counting k x n reduced Latin rectangles) for small k. Specifically, I have in mind conjecture about divisors of these numbers and more data for R(5,n) would support (or, if I'm wrong, not support) this conjecture.

I've written c code and uploaded it

here. It implements

Doyle's formula in the cases R(4,n), R(5,n) and R(6,n), which I have used to find previously unknown values of these numbers. It's not very optimised and I'm wondering if anyone here would be able and willing to help out.

It uses GMP, which I'm told is pretty slow. It doesn't use anything too fancy, eg. multiplication, division, factorials. Since I'm only interested in prime-power divisors of these numbers, it might be possible to only run this code modulo 2^N and then again for 3^N, hopefully eliminating the need for GMP (although I'd prefer to know the numbers exactly if possible).

Anyway, I'm just looking for expressions of interest and an idea of what's possible at the moment... I know there's a lot of people here with expertise in coding.