Seeking general solution for Graeco-Latin Squares of order 4N+2 with N>1

[Matti]

Greetings from a newbie here to MHB. I am a director of a duplicate bridge club, and would like to be able to generate movements when the number of tables is 10, 14, 18 etc. I am aware that the most convenient movements are equivalent to Graeco-Latin Squares, and that these exist for all orders other than 2 and 6.

I can readily generate movements for all odd numbers, and all numbers divisible by 4. I have an example for 10, which I believe is the one which first disproved Euler's Conjecture; but I would like to know if there is a general solution for 10, 14, 18 etc. As far as I am aware, the duplicate bridge world is unaware of one, and would undoubtedly find it useful if it exists!

 

[Valkarie]

If there is no general solution, then I would be grateful for any advice on how to tackle the problem. I am comfortable with coding in C++, and have written a simple program to generate movements for 10 tables (it's more complex than it sounds!). Thanks in advance!