A137348 Number of Steiner quadruple systems (SQS's) of order n.

1, 1, 0, 1, 0, 0, 0, 30, 0, 2520, 0, 0, 0, 37362124800, 0, 14311959985625702400, 0, 0, 0

Offset

1,8

Comments

The values are calculated by utilizing the Knuth's Algorithm X. Only the number of non-isomorphic SQS's is presented in peer-reviewed literature and scientific textbooks. The algorithm was verified to be valid by seeking STS's presented in A001201.

n=14 calculated from "Mendelsohn and Hung: On Steiner Systems S(3,4,14) and S(4,5,15), Util. Math. Vol 1 (1972), pp. 5-95" with orbit-stabilizer theorem

n=15 is given in "Petteri Kaski, Patric R. J. Östergård (Patric.Ostergard(AT)hut.fi) and O. Pottonen, The Steiner quadruple systems of order 16". SQS(20) is still unknown.

References

Petteri Kaski, Patric R. J. Östergård (Patric.Ostergard(AT)hut.fi) and O. Pottonen, The Steiner quadruple systems of order 16

N. S. Mendelsohn and S. H. Y. Hung, On the Steiner Systems S(3,4,14) and S(4,5,15), Util. Math. Vol. 1, 1972, pp. 5-95

Links

Table of n, a(n) for n=1..19.

Vesa Linja-aho, Home Page.

Vesa Linja-aho, Python program

Index entries for sequences related to Steiner systems

Example

There are 2520 SQS's on 10 points.

Crossrefs

Sequence in context: A361058 A198805 A030128 * A137737 A262706 A062513

Adjacent sequences: A137345 A137346 A137347 * A137349 A137350 A137351

Keyword

hard,nonn

Author

Vesa Linja-aho (vesa.linja-aho(AT)tkk.fi), Apr 08 2008, May 13 2008

Status

approved