Classification of Steiner Triple Systems of order 19

The Steiner Triple Systems of order 19, STS(19), were classified by Petteri Kaski and Patric Östergård in 2004 [1]; there are 11,084,874,829 such systems. In 2009, Kaski, Östergård, Olli Pottonen and Lasse Kiviluoto developed a compression algorithm in order to store the data and make it available [2]. Now it is available on this site.

For more information about the classification and compression algorithms, see the papers in bibliography below. If you find this data useful for your research, please cite our paper [2] in your relevant publications.

This page is maintained by Olli Pottonen.

Software and metadata

In version 1.0 of the software, random sampling used a really poor random number generation method. This is fixed in version 1.1.

The data

Here are random samples of distinct STS's, compressed just as the main data set.

Below is all the data. Please note that each file is 400 to 450 megabytes (except the last one which is bit smaller), and the total amount of data is about 39 gigabytes. Download will take time.

Small triple systems

Is trivial that STS(3) is unique. It is also easy to derive the unique of STS(7). The STS(9), STS(13) and STS(15) are more complicated. Regardless even the STS(15) were classified manually [3, 4], which was quite an achievement. Of course later the result has been verified with digital computers several times, first time already in 1955 [5].

These systems are in the files below. The format is different; the (de)compression software is customized for v=19, and for smaller order efficient compression is non-issue. The files are in ASCII, one system on each line. The point set is {a, b, c, … o} (for v=15; for smaller v an obvious subset). The first three characters are the first block, next three characters the second block etc.


  1. P. Kaski and P. R. J. Östergård, The Steiner triple systems of order 19, Math. Comp. 73 (2004), 2075–2092, doi:10.1090/S0025-5718-04-01626-6.
  2. P. Kaski, P. R. J. Östergård, O. Pottonen, L. Kiviluoto, A Catalogue of the Steiner Triple Systems of Order 19, Bulletin of the Institute of Combinatorics and its Applications 57 (2009), 35–41.
  3. F. N. Cole, L. D. Cummings, H. S. White, The complete enumeration of triad systems in 15 elements, Proceedings of the National Academy of Sciences of the United States of America 3 (1917), 197–199.
  4. H. S. White, F. N. Cole, L. D. Cummings, Complete classification of triad systems on fifteen elements, Memoirs of the National academy of Sciences of the United States of America 14 (1919), 1–89.
  5. M. Hall, Jr. J. D. Swift, Determination of Steiner triple systems of order 15, Mathematical Tables and other Aids to Computation 9 (1955), 146–152.