Self-converse Mendelsohn designs with odd block size

Self-converse Mendelsohn designs with block size 6q

A Mendelsohn design lv! D( v, k, A) is a pair (X, B) where X is a v-set together with a collection B of cyclic k-tuples from X such that each ordered pair from X is contained in exactly A cyclic k-tuples of B. An M D(v, k, A) is said to be self-converse, denoted by SC1\ID(v,k,A) = (X,B,f), if there is an isomorphism f from (X, B) to (X, B-1), where B1 = {(:Ek,:r:k-l, ""X2,Xl!: (:1:1, ""Xk! E B}...

Perfect Mendelsohn designs with block size six

Block designs for symmetric parallel line assays with block size odd

SUMMARY. In a parallel line assay, there are three treatment contrasts of major importance. Block designs allowing the estimability of all the three contrasts free from block effects, called L-designs, necessarily have the block sizes even. For odd block sizes, we provide here a class of highly efficient designs, called nearly L-designs. These nearly L-designs have been constructed by establish...

Note on the parameters of balanced designs

In discussing block designs we use the usual notations and terminology of the combinatorialliterature (see, for example, [1], [2]) "balance" will always mean pairwise balance and blocks do not contain repeated elements. It is well-known that a balanced design need not have constant block-size or constant replication number. However, it is easy to show ([2, p.22J). that in any balanced design wi...

Constructions of simple Mendelsohn designs

A Mendelsohn design M(k,v) is a pair (V,B) t where IV\=v and B is a set of cyclically ordered k-tuples of distinct elements of V, called blocks, such that every ordered pair of distinct elements of V belongs to exactly one block of B. A M( k, v) is called cyclic if it has an automorphism consisting of a single cycle of length v. The spectrum of existence of cyclic M(3,v)'s and M(4,v)'s is known...