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A cyclic S- ( 13, 6, 4) design is constructed and is extended to a simple 6-( 14, 7,4) design via a theorem of Alltop. This design is the smallest possible nontrivial simple 6-design that can exist. Both have full automorphism group cyclic of order 13.doi:10.1016/0097-3165(86)90064-6 fatcat:wtzcorkzofewtpeql22de5byta