A 193-self-orthogonal Latin square of order 14
A Latin square of order n is r-self-orthogonal if it and its transpose are r-orthogonal, i.e. their superposition yields exactly r distinct ordered pairs. The spectrum of r-self-orthogonal Latin squares was determined for every order except n = 14, where the single value r = 14² − 3 = 193 remained undecided. This note exhibits a 193-self-orthogonal Latin square of order 14, settling this case and completing the spectrum of r-self-orthogonal Latin squares. A self-contained verification script is included.
Authors
- Changmin Lee
- Minjun Park (ORCID: https://orcid.org/0009-0009-9813-3947)
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-06-26
- DOI
- https://doi.org/10.5281/zenodo.20884696
- Primary Topic
- graph theory and CDMA systems
- Type
- preprint