New semiregular divisible difference sets

New semiregular divisible difference sets

We modify and generalize the construction by McFarland (1973) in two different ways to construct new semiregular divisible difference sets (DDSs) with 21 ~ 0. The parameters of the DDS fall into a family of parameters found in Jungnickel (1982), where his construction is for divisible designs. The final section uses the idea of a K-matrix to find DDSs with a nonelementary abelian forbidden subg...

Factorisation of semiregular relative difference sets

Pott has shown that the product of two semiregular relative difference sets in commuting groups El and E2 relative to their intersection subgroup C is itself a semiregular relative difference set in their amalgamated direct product. We generalise this result in the case that C is central in El and in E2 by using an equivalence with corresponding co cycles 7./Jl and 'l/J2' We prove that in the c...

A Note on New Semi-Regular Divisible Difference Sets

We give a C0051JUCtion for new families of semi-regular divisible difference sets. The construction iJ a variation of McFarland's scheme [Sl tor nonc;yclic difference SCIS. • Let G be a group of order 11111 and N a subgroup of G of order n. If D is a k-subset of G then Dis a {m, n, le , >.1, >.2) divisible difference set in G relative to N provided that the differences dd'1 fur d, d ' ED, d ;e ...

Some nonexistence results on divisible difference sets

Semiregular group divisible designs whose duals are semiregular

ABSTRAC"T A construction method for semiregular group divisible designs is given. This method can be applied to yield many classes of (in general, non-symmetric) semiregular group divisible designs whose duals are semiregular group divisible. In particular, the method can be used to construct many classes of transversal designs whose duals are serniregular group divisible designs, but not trans...