Motzkin-Rabin Geometries

The following files contain lists of all Motzkin-Rabin geometries known to me. The gunzip'ed files have one line per geometry. Each geometry is represented by essentially a base 64 encoding of the incidence matrix. For a precise definition of the encoding see the Decode function in the Embed.m magma file below.

All 12 point geometries (1 geometry, 62 bytes).
All 13 point geometries (1 geometry, 65 bytes).
All 14 point geometries (2 geometries, 126 bytes).
All 15 point geometries (6 geometries, 271 bytes).
All 16 point geometries (18 geometries, 715 bytes).
All 17 point geometries (82 geometries, 3.5K bytes).
All 18 point geometries (1000 geometries, 51K bytes).
Some 19 point geometries (13331 geometries, 769K bytes).
Some 20 point geometries (791085 geometries, 57M bytes).

The undelying linear spaces are contained in these files:

The 12 point linear spaces (1, 62 bytes).
The 13 point linear spaces (1, 65 bytes).
The 14 point linear spaces (2, 123 bytes).
The 15 point linear spaces (5, 232 bytes).
The 16 point linear spaces (5, 243 bytes).
The 17 point linear spaces (36, 1.8K bytes).
The 18 point linear spaces (595, 33K bytes).
The 19 point linear spaces (8266, 509K bytes).
The 20 point linear spaces (759473, 51M bytes).

Here are the Magma programs for embedding linear spaces in projective planes over fields. The file also contains a function for decoding the data files and should be easy to rewrite in almost any programming language.

Paul van Wamelen

Last modified: Tue Aug 16 12:10:20 CDT 2005