On Howell designs

Howell Designs with Sub-designs

A Howell design of side s and order 2n, or more briefly an H(s, 2n), is an s x s array in which each cell is either empty or contains an unordered pair of elements from some (2n)-set V such that (1) every element of V occurs in precisely one cell of each row and each column, and (2) every unordered pair of elements from V is in at most one cell of the array. It follows immediately from the defi...

Sequencings and Howell Designs

On generalized Howell designs with block size three

In this paper, we examine a class of doubly resolvable combinatorial objects. Let t, k, λ, s and v be nonnegative integers, and let X be a set of v symbols. A generalized Howell design, denoted t-GHDk(s, v;λ), is an s × s array, each cell of which is either empty or contains a k-set of symbols from X, called a block, such that: (i) each symbol appears exactly once in each row and in each column...

The Existence of Howell Designs of Even Side

Grosse and R . Rodney Howell

BACKGROUND: Although newborn screening for critical congenital heart disease (CCHD) was recommended by the US Health and Human Services Secretary’s Advisory Committee on Heritable Disorders in Newborns and Children to promote early detection, it was deemed by the Secretary of the HHS as not ready for adoption pending an implementation plan from HHS agencies. OBJECTIVE: To develop strategies for...