Super-simple [formula omitted] designs

Abstract

Super-simple designs are useful in constructing codes and designs such as superimposed codes and perfect hash families. Recently, Gronau et al. determined the existence of super-simple ( v , 5 , 2 ) -BIBDs with possible exceptions of v ∈ { 75 , 95 , 115 , 135 , 195 , 215 , 231 , 285 , 365 , 385 , 515 } . In this article, we investigate the existence of a super-simple ( v , 5 , 4 ) -BIBD and show that such a design exists if and only if v ≡ 0 , 1 ( mod 5 ) and v ⩾ 15 . In addition, we also constructed a super-simple ( v , 5 , 2 ) -BIBD for v = 75 , 95 , or 385.