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 A137348 Number of Steiner quadruple systems (SQS's) of order n. 1

%I

%S 1,1,0,1,0,0,0,30,0,2520,0,0,0,37362124800,0,14311959985625702400,0,0,

%T 0

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

%C 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.

%C 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

%C 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.

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

%D 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

%H Vesa Linja-aho, <a href="/A137348/a137348.txt">Python program</a>

%H <a href="/index/St#Steiner">Index entries for sequences related to Steiner systems</a>

%e There are 2520 SQS's on 10 points.

%K hard,nonn

%O 1,8

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

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Last modified July 27 05:04 EDT 2021. Contains 346305 sequences. (Running on oeis4.)