Latest additions and changes
- 6th January 2007
- The links to the references are now working, but pop-up restrictions may affect the appearance.
- 11th December 2006
- Many changes to the construction of nested 3-designs, seehere
- For some reason, the links to the references are no longer working properly. I will try to fix this asap.
- 24th March 2006
- Some more geometrical constructions, based on quadratics and similar objects. Most of these are
well-known, put in for completeness. See here.
- 4th October 2005
- An erroneous conjecture (for the analysis of projective geometries
with nested sub-geometries) has been removed (at the second attempt).
Some examples have been given instead. See here.
- 23rd May 2005
- An amendment on the table of small NBIBDs for
v=7
- Note that some of the group sizes etc for the resolved BIBD
searches are incorrect. I haven't worked out why as yet.
- 19th October 2004
- The results of more searches (so far, for BIBDs only) have been
added, and more details given. In particular, details of automorphism
groups and block intersections are shown for the latest cases.
- Some searches based on groups other than the integers mod n (Zn)
have been included.
- 15th July 2004
- I have removed a lot of superfluous stuff.
- 30th April 2004
- Correction of error in table for projective geometries PG(k,q2ν), k>2here.
- Plane of type B1 from PG(3,q2ν)here
- Hyperplane of type D1 from PG(4,q2ν)here
- 20th April 2004
- Discussion of planes PG(2,qρν) with composite ρ here
- 30th March 2004
- A start on a 4-dimensional geometry (for q=2 only) here.
- Two 3-dimensional spaces from the above, with 3 and 7 points of the subgeometry.
- Three planes from one of the above, with 0, 1 and 3 points of the subgeometry.
- More detail, and some corrections to errors, on the 3-dimensional geometry here.
- 5th March 2004
- A second plane of type B1 for q=3 here.
- 3rd March 2004
- A plane of type B3 for q=3 here plus some corrections
to typographical errors.
- 22nd February 2004
- Some more bits of geometric constructions here, going
further into 3 dimensions, with some new types of 2-dimensional constructions.
- 9th December 2003
- Some more bits of geometric constructions here, going
into 3 dimensions, with some consequential 2-dimensional constructions as well.
Note that the notation has been changed throughout this section.
- 19th November 2003:
- 2 missing cases of (3,6)NBIBDs - for v = 58,138. This leaves 18 still to be solved.
- Some geometric constructions, with associated references, of PBDs and some GDDs (potentially lots more).
- 10th September 2003:
- Completion of new menu system, almost. It doesn't work properly for the two XML
pages: this (minor) problem will be tackled in due course.
- Minor textual changes here and there, mainly some references to the literature.
- 18th August 2003:
- 28th June 2003:
- An applet indicating how to construct OBIBDs with a block size of 3
(based on Greig & Rees).
- A new section giving some results on the existence of NBIBDs.
- A table showing examples of NBIBDs of small size .
- Some new searches for BIBDs and NBIBDs.
- Previously:
Last Updated: 6th January 2007
By D.H.Rees