Balanced incomplete block designs with block size 9: part II

Balanced incomplete block designs with block size~9: Part III

The necessary conditions for the existence of a balanced incomplete block design on v points, with index λ and block size k, are that: λ(v − 1) ≡ 0 mod (k − 1) λv(v − 1) ≡ 0 mod k(k − 1) Earlier work has studied k = 9 with λ ∈ {1, 2, 3, 4, 6, 8, 9, 12}. In this article we show that the necessary conditions are sufficient for λ = 9 and every other λ not previously studied.

Splitting balanced incomplete block designs

Finding Balanced Incomplete Block Designs with Metaheuristics

This paper deals with the generation of balanced incomplete block designs (BIBD), a hard constrained combinatorial problem with multiple applications. This problem is here formulated as a combinatorial optimization problem (COP) whose solutions are binary matrices. Two different neighborhood structures are defined, based on bit-flipping and position-swapping. These are used within three metaheu...

Non-Isomorphic Solutions of Some Balanced Incomplete Block Designs II

Some techniques are developed for constructing non-isomorphic solutions of symmetric (4t + 3,2t + 1, t) designs for suitable values of t and for (4t + 2, 8t + 2,4t + 1,2t + 1,2t) and (4t + 4, St + 6,4t + 3,2t + 2,2t + 1) designs. As an application, some non-isomorphic solutions of (19,9,4), (10,18, 9, 5, 4), and (12, 22, 11, 6, 5) designs are obtained. In [l] some other techniques were given fo...

Super-Simple Resolvable Balanced Incomplete Block Designs with Block Size 4 and Index 4

The necessary conditions for the existence of a super-simple resolvable balanced incomplete block design on v points with block size k = 4 and index λ = 2, are that v ≥ 16 and v ≡ 4 (mod 12). These conditions are shown to be sufficient. © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 341–356, 2007