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

Author

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

Keywords

• hard
• nonn

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.

Examples

			There are 2520 SQS's on 10 points.
		

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

• Vesa Linja-aho, Home Page.
• Vesa Linja-aho, Python program
• Index entries for sequences related to Steiner systems