Hadamard transform

Engineering

Affine space

Affine transformation

Aerospace engineering

Pure mathematics

Discrete mathematics

Set (abstract data type)

Computer science

Upper and lower bounds

Affine hull

Mathematics

Block design

Mathematical analysis

Artificial intelligence

Geometry

Combinatorics

Point (geometry)

Programming language

Intersection (aeronautics)

Class (philosophy)

Line (geometry)

Discrete Mathematics

A line of a design is the intersection of all the blocks on two points. There is an upper bound on the number of points in a line of a design. A line of a design which meets this upper bound is said to be of maximal length. Restrictions are obtained on the parameters of a symmetric 2-design in order that it might possess a set of lines of maximal length which partitions the point set of the design (that is, a ‘1-spread’). It is shown that the existence of an affine resolvable design with four blocks in each affine resolution class is equivalent to the existence of a Hadamard design possessing a 1-spread. Two recursive constructions for affine resolvable designs with four blocks in each affine resolution class are also given.

On the line structure of designs