[GAP Forum] Block designs online

[Leonard Soicher]

This is to announce an major upgrade of the DesignTheory.org collections of
block designs and their combinatorial, group-theoretical and statistical
properties, available from  http://designtheory.org/database/ .  

The `t-designs' collection now (properly) contains, up to isomorphism, all
cyclic and all 1-rotational 2-designs with 6<=v<=20, r<=20 and 3<=k<=v/2.
Many of these designs are new.

The `v-b-k' collection now consists of all binary connected block designs
(up to isomorphism) with v points, b blocks and constant block size k,
such that  v,b,k >= 2  and  v+b <= 16.  Moreover, the (lexicographically
sorted) block-list of each design in this collection is lexicographically
least in its isomorphism class.

Using the `v-b-k' collection, we now give all binary connected block
designs which are phi_0-optimal (D-optimal), phi_1-optimal (A-optimal),
phi_2-optimal, MV-optimal or E-optimal, such that  v,b,k >= 2  and  
v+b <= 16.

The `v-b-r-k' collection presently consists of all binary connected block
designs (up to isomorphism) with v points, b blocks, constant replication
number r and constant block size k, such that v,b,r,k >= 2 and v+b <= 18.

The present collections are the result of joint work by Peter
Dobcsanyi and Leonard Soicher in the development and application
of the DesignTheory.org software packages, freely available
from http://designtheory.org/software/ .  The block designs and
their properties are in DTRS protocol version 2.0 XML-format; see
http://designtheory.org/library/extrep/ .  This protocol and our python
and GAP software packages can be used for the input, output, generation,
classification and study of block designs.

More designs will be uploaded in due course by members of the
DesignTheory.org team.  Contributions of block designs in the DTRS
XML-format are welcome, and you will get full credit for these.
Please also email me any comments, especially if you find any errors.
Please link to the DesignTheory.org website, and reference our design
collections and/or software if you make use of them.

Regards,  Leonard Soicher