Nets and Latin Squares of Small Order
This site is intended to provide a list (in some cases exhaustive)
of nets of small order.
In addition to my own C++ programs, I have made use of Brendan McKay's
graph isomorphism package
nauty
in testing for automorphisms and isomorphisms of nets.
A k-net of order n is an incidence system consisting of
n2 points and nk lines such that
- each line has n points and each point is on k lines;
- any two distinct lines meet in either 0 or 1 point;
- parallelism (the relation of two lines being either equal or disjoint)
is an equivalence relation on the lines;
- there are k parallel classes of lines, each with n.
The parameters k and n are the order and the index
of the net. For more information
about nets and Latin squares, please refer to
- T. Beth, D. Jungnickel and H. Lenz,
Design Theory, Cambridge Univ. Press, 1986
- The CRC Handbook of Combinatorial Designs, ed. C.J. Colbourn and
J.H. Dinitz, CRC Press, 1996
While many lists of nets have been compiled by others, my main purpose
here is to investigate p-ranks of nets.
If you are aware of errors or omissions
in my list, I would appreciate an email
message (
) from you.
Complete Lists of Nets
Here we provide complete lists of nets of small order, as found by
exhaustive backtrack search.
Incomplete Lists of Nets
/
revised April, 2001
