Some 2-(2n+1,n,n-1) designs with multiple extensions

Abstract

A 2-(2n+1,n,λ) design can always be extended to a 3-(2n+2,n+1,λ) design by complementation. If λ is large enough there may.be other methods of extension. By constructing non-self-complementary 3-(18,9,7) designs it is shown that there is a 2-(17,8,7) design with 16 extensions. The method generalises to construct non-self complementary 3-(2n+2,n+1,n-1) designs for larger values of n.