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The existence of simple \(6\text{-}(14,7,4)\) designs. (English) Zbl 0647.05013
Summary: A cyclic \(5\text{-}(13,6,4)\) design is constructed and is extended to a simple \(6\text{-}(14,7,4)\) design via a theorem of W. O. Alltop [ J. Comb. Theory, Ser. A 18, 177–186 (1975; Zbl 0297.05028)]. This design is the smallest possible nontrivial simple 6-design that can exist. Both have full automorphism group cyclic of order 13.

MSC:
05B05 Combinatorial aspects of block designs
20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures
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