On 2-designs

On 2-Designs

Denote by M,, the set of integers h for which there exists a 2-design (linear space) with r points and h lines. M,, is determined as accurately as possible. On one hand, it is shown for r > r " that M, contains the interval [r+r° s , (_)-4 ]. On the other hand for r of the form p'-+p+ I it is shown that the interval [u+ 1, r+p-I] is disjoint from M, ; and if r > r " and p is of the form q'-+y, ...

Construction of Designs on the 2-Sphere

Spherical r-designs are Chebyshev-type averaging sets on the d-dimensional unit sphere Sd-l that are exact for all polynomials of degree at most t. The concept of such designs was introduced by Delsarte , Goethals and Seidel in 1977. The existence of spherical designs for every t and d was proved by Seymour and Zaslavsky in 1984. Although some sporadic examples are known, no general constructio...

ibn 2 - TRANSITIVE DESIGNS

Halving Steiner 2-designs

A Steiner 2-design S(2,k,v) is said to be halvable if the block set can be partitioned into two isomorphic sets. This is equivalent to an edge-disjoint decomposition of a self-complementary graph G on v vertices into Kks. The obvious necessary condition of those orders v for which there exists a halvable S(2,k,v) is that v admits the existence of an S(2,k,v) with an even number of blocks. In th...

Semifolding 2 Designs

This article addresses the varied possibilities for following a two-level fractional factorial with another fractional factorial half the size of the original experiment. While follow-up fractions of the same size as an original experiment are common practice, in many situations a smaller follow-up experiment will suffice. Peter John coined the term “semifolding” to describe using half of a fol...