Projective Planes of Order 49

This site, currently under construction (May 2009), is intended to provide a current list of known projective planes of order 49, similar to my lists for other small orders. This work starts with the classification of the 1347 translation planes of order 49, due to Mathon and Royle, and independently verified by Dempwolff and Charnes.

• R. Mathon, G. Royle, ‘The translation planes of order 49’, Designs, Codes and Cryptography 5 (1995), 52–72. Royle's website
• U. Dempwolff, C. Charnes, ‘The translation planes of order 49 and their automorphism groups’, Math. of Computation 67 (1998), 1207–1224. Dempwolff's website

I currently have several processes on a local cluster devoted to enumerating the various derived planes, planes formed by lifting quotients, etc. and the list is steadily growing. Check back soon for updates!

Already it seems that most of these planes have full collineation group of order 4116=2²*3*7³, just as most of the known planes of order 25 have full collineation group of order 500=2²*5³. More details will be appearing soon...

As of June 26, 2009, my list includes over twenty thousand planes of order 49. This list is growing at the rate of 3 or 4 new planes per hour, so listing a current count here is meaningless. I expect my program to continue through most of the summer, yielding maybe 10⁵ or 10⁶ nonisomorphic planes of order 49.

/ revised June, 2009