The Steiner quadruple systems of order 16
نویسندگان
چکیده
منابع مشابه
The Steiner quadruple systems of order 16
The Steiner quadruple systems of order 16 are classified up to isomorphism by means of an exhaustive computer search. The number of isomorphism classes of such designs is 1,054,163. Properties of the designs—including the orders of the automorphism groups and the structures of the derived Steiner triple systems of order 15—are tabulated. A double-counting consistency check is carried out to gai...
متن کاملClassification of steiner quadruple systems of order 16 and rank 14
A Steiner quadruple system S(v, 4, 3) of order v is a 3-design T (v, 4, 3, λ) with λ = 1. In the previous paper [1] we classified all such Steiner systems S(16, 4, 3) of order 16 with rank 13 or less over F 2. In particular, we have proved that there is can be obtained by the generalized doubling construction, which we give here. Our main result is that there are exactly 684764 non-isomorphic S...
متن کاملThe existence of resolvable Steiner quadruple systems
A Steiner quadruple system of order v is a set X of cardinality v, and a set Q, of 4-subsets of X, called blocks, with the property that every 3-subset of X is contained in a unique block. A Steiner quadruple system is resolvable if Q can be partitioned into parallel classes (partitions of X). A necessary condition for the existence of a resolvable Steiner quadruple system is that v = 4 or 8 (m...
متن کاملClassification of Flag-Transitive Steiner Quadruple Systems
A Steiner quadruple system of order v is a 3 − (v, 4, 1) design, and will be denoted SQS(v). Using the classification of finite 2-transitive permutation groups all SQS(v) with a flag-transitive automorphism group are completely classified, thus solving the ”still open and longstanding problem of classifying all flag-transitive 3− (v, k,1) designs” (cf. [5, p. 273], [6]) for the smallest value o...
متن کاملAffine-invariant strictly cyclic Steiner quadruple systems
A Steiner quadruple system of order v, denoted by SQS(v), is a pair (V, B), where V is a finite set of v points, and B is a collection of 4-subsets of V , called blocks or quadruples, such that each 3-subset (triple) of V is contained in exactly one block in B. An automorphism group of SQS(v) is a permutation group on V leaving B invariant. An SQS(v) is said to be cyclic if it admits an automor...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2006
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2006.03.017