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

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-06-26
DOI
https://doi.org/10.5281/zenodo.20884695
Primary Topic
graph theory and CDMA systems
Type
preprint
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preprint

A 193-self-orthogonal Latin square of order 14

Changmin Lee, Minjun Park
Zenodo (CERN European Organization for Nuclear Research)
graph theory and CDMA systems
preprint

A 193-self-orthogonal Latin square of order 14

Changmin Lee, Minjun Park
preprint en

Abstract

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.

Zenodo (CERN European Organization for Nuclear Research)
graph theory and CDMA systems
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A 193-self-orthogonal Latin square of order 14 — Changmin Lee, Minjun Park · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS