2 citations · 3 across the 2 of their papers we have counts for
14 papers
Integer and Constraint Programming Revisited for Mutually Orthogonal Latin Squares
Noah Rubin, Curtis Bright, Kevin K. H. Cheung +1
In this paper we provide results on using integer programming (IP) and constraint programming (CP) to search for sets of mutually orthogonal latin squares (MOLS). Both programming…
Nonexistence Certificates for Ovals in a Projective Plane of Order Ten
Curtis Bright, Kevin K. H. Cheung, Brett Stevens +2
In 1983, a computer search was performed for ovals in a projective plane of order ten. The search was exhaustive and negative, implying that such ovals do not exist. However, no no…
Unsatisfiability Proofs for Weight 16 Codewords in Lam's Problem
Curtis Bright, Kevin K. H. Cheung, Brett Stevens +2
In the 1970s and 1980s, searches performed by L. Carter, C. Lam, L. Thiel, and S. Swiercz showed that projective planes of order ten with weight 16 codewords do not exist. These se…
A Nonexistence Certificate for Projective Planes of Order Ten with Weight 15 Codewords
Curtis Bright, Kevin Cheung, Brett Stevens +3
Using techniques from the fields of symbolic computation and satisfiability checking we verify one of the cases used in the landmark result that projective planes of order ten do n…
Complex Golay Pairs up to Length 28: A Search via Computer Algebra and Programmatic SAT
Curtis Bright, Ilias Kotsireas, Albert Heinle +1
We use techniques from the fields of computer algebra and satisfiability checking to develop a new algorithm to search for complex Golay pairs. We implement this algorithm and use…
The SAT+CAS Method for Combinatorial Search with Applications to Best Matrices
Curtis Bright, Dragomir Ž. Đoković, Ilias Kotsireas +1
In this paper, we provide an overview of the SAT+CAS method that combines satisfiability checkers (SAT solvers) and computer algebra systems (CAS) to resolve combinatorial conjectu…