This page provides access to the (known) projective planes of order 16, along with a smallish amount of associated data. I am always happy to provide additional useful information for researchers, so please mail me at gordon@cs.uwa.edu.au if you want anything.
The 242K gzipped tar file planes16.tar.gz contains everything mentioned on the remainder of the page. This is essentially a copy of the directory that used to be available via ftp before the disk exploded. Read the file INDEX for help.
These are the names of the known planes of order 16.
| Plane Name | Description |
|---|---|
| PG(2,16) | The desarguesian projective plane of order 16 |
| SEMI2 | The semifield plane with kernel GF(2) |
| SEMI4 | The semifield plane with kernel GF(4) |
| HALL | The Hall plane |
| LMRH | The Lorimer-Rahilly plane |
| JOWK | The Johnson-Walker plane |
| DSFP | The derived semifield plane |
| DEMP | The Dempwolff plane |
| JOHN | The Johnson plane |
| BBS4 | Plane derived from the (dual of) SEMI4 from a derivation set of Bose-Barlotti type not on the (dual) translation line |
| BBH2 | Plane derived from the dual of HALL from a derivation set of Bose-Barlotti type "from a line not on the regulus" |
| MATH | The Mathon plane |
| BBH1 | Plane derived from the dual of HALL from a derivation set of Bose-Barlotti type "from a line on the regulus" |
The following table gives the blocks of the known planes of order 16. The links under the names give the blocks for the plane or for its dual (if not self dual).
| No. | Plane Name | Dual Plane | Group size | Orbit sizes | Info. |
|---|---|---|---|---|---|
| 0 | PG(2,16) | 2^15.3^3.5^2.7.13.17 | {546} | Orbits | |
| 1 | SEMI2 | 147456 | {2, 32, 512} | Orbits | |
| 2 | SEMI4 | 884736 | {2, 32, 512} | Orbits | |
| 3 | HALL | HALL | 921600 | {5, 12, 256 | 1, 80, 192} | Orbits |
| 4 | LMRH | LMRH | 258048 | {3, 14, 256 | 1, 48, 224} | Orbits |
| 5 | JOWK | JOWK | 258048 | {3, 14, 256 | 1, 48, 224} | Orbits |
| 6 | DSFP | DSFP | 55296 | {2, 3, 12, 256 | 1, 32, 48, 192} | Orbits |
| 7 | DEMP | DEMP | 92160 | {1, 1, 15, 256 | 1, 16, 16, 240} | Orbits |
| 8 | JOHN | JOHN | 2304 | {2, 3, 12, 16, 48, 96, 96 | 1, 8, 12 12, 24, 24 192} | Orbits |
| 9 | BBS4 | BBS4 | 3456 | {2, 3, 12, 16, 96, 144 | 1, 8, 12, 24, 36, 192} | Orbits |
| 10 | BBH2 | BBH2 | 3840 | {5, 12, 16, 80, 160 | 1, 20, 20, 40, 192} | Orbits |
| 11 | MATH | MATH | 12288 | {1, 16, 256 | 1, 16 256} | Orbits |
| 12 | BBH1 | 18432 | {2, 8, 24, 128, 384} | Orbits | |
Gordon Royle, gordon@cs.uwa.edu.au, March 1997