The Dual of a Balanced Incomplete Block Design

Self-Dual Codes and the (22,8,4) Balanced Incomplete Block Design

We enumerate a list of 594 inequivalent binary (33, 16) doubly-even self-orthogonal codes that have no all-zero coordinates along with their automorphism groups. It is proven that if a (22, 8, 4) Balanced Incomplete Block Design were to exist then the 22 rows of its incident matrix will be contained in at least one of the 594 codes. Without using computers, we eliminate this possibility for 116...

Splitting balanced incomplete block designs

Calculating Balanced Incomplete Block Design for Educational Assessments

A popular design in large scale' educational assessments is the balanced incomplete block design. The design assumes that the item pool is split into a set of blocks of items that are assigned to assessment booklets. This paper shows how the technique of 0-1 linear programming can be used to calculate a balanced incomplete block design. Several structural as well as practical constraints on thi...

A-efficient balanced treatment incomplete block designs

The purpose of this paper is to present a large number of highly A-efficient incomplete block designs for making comparisons among a set of test treatments and a control treatment. These designs are BTIB designs. A simple method of construction of BTIB designs, based on BIB designs is proposed. The advantage of this method is that one can use the vast literature on BIB designs to obtain a large...

Minimum embedding of a P4-design into a balanced incomplete block design of index lambda

Let H be a subgraph of G. An H-design (V, C) of order v and index μ is embedded into a G-design (X,B) of order v + w and index λ if μ ≤ λ, V ⊆ X and there is an injective mapping f : C → B such that B is subgraph of f (B) for every B ∈ C. For every pair of positive integers v, λ, (except when λ = 3 and v = 30, 34, 42, 46, 54, 58, 66 or λ = 5 and v = 19) we determine the minimum value of w such ...