Construction of Balanced Incomplete Block Designs: Construcción de Diseños de Bloques Incompletos Balanceados
Saved in:
| Authors: | , |
|---|---|
| Format: | artículo original |
| Status: | Versión publicada |
| Publication Date: | 2026 |
| Description: | In this review article, we study balanced incomplete block designs (BIBDs) and test a heuristic algorithm for generating these designs. We first provide a brief theoretical exposition of BIBDs,the mathematical properties of which are of extreme importance due to their deep theoretical applications in non-Euclidean geometry (construction of finite projective and finite affine planes) and incombinatorics. We use a simulated annealing algorithm to find BIBDs of moderate size. In particular,we discover a new, unpublished solution for the BIBD(16,56,21,6,7), for which only one other solutionwas known, even though the theoretical existence of more solutions was certain. Our algorithms werecompared with other heuristic methods used in previous research and consistently outperformed allother heuristic methods. |
| Country: | Portal de Revistas TEC |
| Institution: | Instituto Tecnológico de Costa Rica |
| Repositorio: | Portal de Revistas TEC |
| Language: | Español |
| OAI Identifier: | oai:ojs.pkp.sfu.ca:article/8771 |
| Online Access: | https://revistas.tec.ac.cr/index.php/matematica/article/view/8771 |