With that definition, a 3-net is the same as a latin square. The rows are the lines of one pencil. The columns are the lines of the second pencil. And the set of all the entries with the same number are the lines of the thirthd pencil. The points would be the entries of the square.
Also, you can construct them geometrically over an affine plane... but not over the reals. It can be done over finite fields. El Martes, 20 de agosto de 2013 16:24:54 muhammad shah escribió: > Dear Arun, > Excellent GAP codes for 3-web written by Dr. Petr are available at > http://web.cs.du.edu/~petr/gap_routines.html > (3-Webs and basic operations on 3-Webs) > and for a nice visualization of 3-web see the paper of > H. I. Erdorgan (A QUASI-GROUP ASSOCIATED WITH THE WEB > FORMED BY THREE PENCILS OF CIRCLES WHICH > BELONG TO THE SAME BIJNDLE). > Regards, > Muhammad Shah > > Date: Tue, 20 Aug 2013 00:30:28 -0700 > From: amukti2...@yahoo.com > To: group-pub-fo...@lists.maths.bath.ac.uk > Subject: [group-pub-forum] 3-net > > Dear Pubbers, I am not able to visualize a 3-net of order 3. Taking three mutually disjoint sets of non-intersecting lines , every line should pass through 3 points and every point should lie on exactly one line of each class. Can anybody give an example with a diagram ? Thanking you in advance.ArunIndia Dr. Arun Muktibodh > _______________________________________________ > Forum mailing list > Forum@mail.gap-system.org > http://mail.gap-system.org/mailman/listinfo/forum _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
