ODLK1
ODLK1 is a volunteer distributed computing project that needs your help to investigate diagonal Latin squares.
Goal
BOINC project ODLK1 continues to solve the problem of BOINC project ODLK. The project generates a database of canonical forms (CF) of diagonal Latin squares (DLS) of order 10 that possess orthogonal diagonal Latin squares (ODLS). In combinatorics, a Latin square of order n is an n × n array in which each of n different symbols appears exactly once in each row and once in each column. A diagonal Latin square additionally requires that both main diagonals also contain each symbol exactly once.[1] Two such squares are orthogonal if, when superimposed, every ordered pair of symbols appears exactly once.[2]
The goal of the project is a complete enumeration of canonical forms of order-10 DLS that have at least one orthogonal partner, contributing to an open problem in combinatorial mathematics with connections to magic square construction, Sudoku-like puzzles, statistical experimental design, and error-correcting codes.
Background
Latin squares and orthogonality
The study of Latin squares dates to Leonhard Euler in the 18th century. Euler conjectured that orthogonal Latin squares of certain orders could not exist; this conjecture was famously disproved for orders greater than 6 in 1960.[3] The additional symmetry constraints imposed by the diagonal condition make the orthogonality question significantly harder at order 10.
A pair of diagonal Latin squares of order 10 are called an orthogonal pair (or MODLS — Mutually Orthogonal Diagonal Latin Squares) when the 100 cells of one, overlaid on the other, produce all 100 distinct ordered pairs of symbols. Such pairs are extremely rare and were unknown until 1992. A canonical form (CF) is a standardised representative of an equivalence class of squares related by symmetry transformations; reducing each square to its canonical form allows researchers to count and catalogue truly distinct configurations without duplication.
Foundational result (1992)
The first three orthogonal pairs of diagonal Latin squares of order 10 were found in 1992 and published in the paper "Completion of the Spectrum of Orthogonal Diagonal Latin Squares" by J. W. Brown, F. Cherry, L. Most, E. Parker, and W. D. Wallis.[4] This result completed the proof that orthogonal diagonal Latin squares of every order except 2 and 6 exist, but left open the question of how many such pairs exist at order 10 and what their full structure looks like.
SAT@home predecessor project (2012–2016)
From 2012 to 2016 the scientific BOINC project SAT@home searched for new orthogonal pairs of diagonal Latin squares of order 10 using Boolean satisfiability (SAT) solving techniques.[5] That project discovered 77 unique orthogonal pairs, yielding 154 unique canonical forms of ODLS. The solutions from SAT@home were incorporated into the ODLK1 database as a starting point.
ODLK — the predecessor BOINC project (2017–present)
The original BOINC project ODLK was launched on 19 May 2017 by Natalia Makarova at https://boinc.progger.info/odlk/, hosted by Progger (Czech Republic).[6] The ODLK project has celebrated successive anniversaries; a post from May 2024 marked its seventh year of continuous operation.[7] The complete database of canonical forms found by the ODLK project from 2017 through January 2022 was published by Natalia Makarova.[8]
History
ODLK1 (also known as LatinSquares) was announced in December 2017 as a Russian-Italian continuation of the ODLK project. On 7 December 2017, Natalia Makarova posted on the BOINC message boards: "Welcome to the Russian-Italian project ODLK1!" with the project hosted by Stefano Tognon (ice00) on the multi-pool.info infrastructure.[9] The project runs alongside its parent, with different server infrastructure, allowing volunteers to contribute to both projects in parallel.
The first application, odlk3@home, became available on Linux (x86-64) on 28 October 2017, with Windows, Linux x86, and FreeBSD versions added on 6 November 2017. A second application, odlkmax@home, was added on 26 December 2017.[10] An ARM64 Linux build of odlk3@home was added on 30 December 2024, showing continued active development and support for modern hardware.[11]
An early progress report covering November 2017 through February 2020 showed the project had processed approximately 8,993,278 total "mate" (DLS with orthogonal partner) squares.[12]
In January 2026 the project migrated to upgraded server hardware; as Stefano Tognon noted, the changeover was handled within the existing virtual machine, so volunteers noticed no interruption except for a brief downtime of approximately one hour.[13]
In February 2025 a new related project, ODLK2025, was launched separately at https://boinc.mak.termit.me/odlk2025/, indicating ongoing community interest in extending this family of research.[14]
Project team / Sponsor
- Natalia Makarova — Scientific author and research lead (Russia). Originator of both the ODLK and ODLK1 projects and author of numerous posts to the OEIS documenting results. Contact: [email protected].[15]
- Progger — Co-maintainer (Czech Republic); responsible for server administration on the parent ODLK project and ongoing liaison with the ODLK1 infrastructure.
- Stefano Tognon (ice00) — Infrastructure host (Italy); operates the multi-pool.info BOINC hosting environment on which ODLK1 runs, and manages server hardware upgrades.
- Reese — Credited co-maintainer, listed in the project copyright since 2024.[16]
Applications
The project currently runs two CPU-only applications, both at version 1.00:[17]
odlk3@home
Searches for canonical forms of order-10 DLS using the odlk3 algorithm. Typical task runtime averages 0.37 hours (ranging 0 to ~58 hours). Supported platforms and benchmark performance:
| Platform | Avg. GigaFLOPS |
|---|---|
| Windows x86-64 | 4,777 |
| Linux x86-64 | 3,764 |
| Linux ARM64 | 431 |
| FreeBSD x86-64 | 448 |
| Windows x86 / Linux x86 / FreeBSD x86 | 6–20 |
odlkmax@home
Focuses on finding DLS of order 10 with the maximum possible number of orthogonal partners. Typical task runtime averages 0.31 hours (ranging 0.01 to ~42 hours). Supported on Windows (x86, x86-64), Linux (x86, x86-64), and FreeBSD (x86, x86-64). Average computing power up to ~4,755 GigaFLOPS on Windows x86-64.
Both applications are purely CPU-based; no GPU acceleration is offered. Task deadlines are seven days; checkpointing is not supported. Recommended RAM per task is approximately 10 MB.
Server status (as of 22 May 2026)
All server components — scheduler, feeder, transitioner, file deleter, db_purge, validators, assimilators, and work generators for both applications — were confirmed running.[18]
| Metric | Value |
|---|---|
| Tasks ready to send | 434,860 |
| Tasks in progress | 195,221 |
| Workunits awaiting validation | 0 |
| Workunits awaiting assimilation | 5 |
| Users with recent credit | 562 |
| Total registered users (with credit) | 3,885 |
| New users in past 24 hours | 70 |
| Hosts with recent credit | 2,687 |
| Total registered hosts (with credit) | 112,444 |
| New hosts in past 24 hours | 21 |
| Current performance | ~18,127 GigaFLOPS |
| Server software version | 1.1.0 |
Tasks by application (22 May 2026)
| Application | Unsent | In progress | Avg. runtime (hours) | Active users (last 24 h) |
|---|---|---|---|---|
| odlk3@home | 197,325 | 101,903 | 0.37 (0 – 57.95) | 287 |
| odlkmax@home | 237,536 | 93,317 | 0.31 (0.01 – 42.05) | 274 |
Scientific results
The primary output of the project is the growing database of canonical forms of order-10 DLS with orthogonal partners, hosted publicly on Yandex Disk:
- https://disk.yandex.ru/d/RsHtIf6bCWV8xg
- Application odlk3: 350,094 CF ODLK discovered
- Application odlkmax: 342,181 CF ODLK discovered
Together these represent a substantial expansion beyond the 154 canonical forms known from SAT@home in 2016, and constitute one of the most comprehensive datasets on orthogonal diagonal Latin squares of order 10 ever compiled.
The OEIS contains multiple sequences informed by research from the ODLK/ODLK1 community, including entries on the number of normalised ODLS derivable from a single DLS and the enumeration of DLS of small orders by various combinatorial properties.[19]
Community and teams
ODLK1 is an internationally participated project. The top contributing teams as of May 2026 by recent average credit are:[20]
| Rank | Team | Members | Recent avg. credit | Total credit |
|---|---|---|---|---|
| 1 | Gridcoin | 1,256 | 1,562,924 | 4,356,244,831 |
| 2 | Ars Technica | 9 | 239,238 | 37,519,798 |
| 3 | Ukraine | 19 | 172,136 | 29,620,446 |
| 4 | Czech National Team | 57 | 70,942 | 75,664,807 |
| 5 | XtremeSystems | 14 | 50,690 | 42,620,371 |
| 6 | UK BOINC Team | 30 | 44,371 | 38,450,478 |
| 7 | Sicituradastra. | 12 | 42,956 | 19,377,308 |
| 8 | BOINC@AUSTRALIA | 28 | 40,745 | 63,603,287 |
| 9 | L'Alliance Francophone | 119 | 39,321 | 90,119,379 |
| 10 | Rechenkraft.net | 44 | 37,467 | 50,012,989 |
The dominant team, Gridcoin, is an open-source cryptocurrency project that rewards BOINC volunteers with GRC tokens in proportion to their computing contribution across whitelisted projects.[21] ODLK1 is included on the Gridcoin whitelist, meaning participants can earn Gridcoin cryptocurrency while contributing to the project's mathematical research.
Top individual contributors (by recent average credit, May 2026)
| Rank | Participant | Country | Recent avg. credit | Member since |
|---|---|---|---|---|
| 1 | macgeyer | France | 426,078 | Jan 2018 |
| 2 | Science United | — | 220,239 | Feb 2019 |
| 3 | whizbang | — | 207,001 | Jul 2025 |
| 4 | grcpool.5 | International | 193,694 | Dec 2022 |
| 5 | KetamiNO [YouTube] | Ukraine | 167,041 | Jan 2019 |
The earliest registered active participant, "klepel" (rank 19), joined on 11 January 2018 — just weeks after the project opened — and continues to contribute as of May 2026.
Related scientific publications
The broader research programme on diagonal Latin squares and their orthogonality, which directly motivates ODLK1, has produced a significant body of peer-reviewed literature. Key papers include:
- Vatutin, E. I.; Zaikin, O. S.; Kochemazov, S. E.; Valyaev, S. Yu..(2017}).Using Volunteer Computing to Study Some Features of Diagonal Latin Squares. Open Engineering. pp. 453–460. DOI: 10.1515/eng-2017-0052. — Presents algorithms for enumerating transversals of DLS and the reduction of the order-10 ODLS search to a SAT problem, with large-scale experiments in Gerasim@home and SAT@home.[23]
- "Applying Volunteer and Parallel Computing for Enumerating Diagonal Latin Squares of Order 9". In:.(2017}).Communications in Computer and Information Science. Springer, Cham. pp. 114–129. DOI: 10.1007/978-3-319-67035-5_9. — First complete enumeration of all DLS of order 9, a previously unsolved problem, using the Gerasim@home BOINC project.[24]
- "Enumeration of Isotopy Classes of Diagonal Latin Squares of Small Order Using Volunteer Computing". In:.(2019}).Communications in Computer and Information Science (RuSCDays 2018). Springer, Cham. pp. 578–586. DOI: 10.1007/978-3-030-05807-4_49.[25]
- "Evaluation of Efficiency of Using Simple Transformations When Searching for Orthogonal Diagonal Latin Squares of Order 10". In:.(2020}).Supercomputing (RuSCDays 2020). Springer, Cham. DOI: 10.1007/978-3-030-66895-2_9.[26]
- Zaikin, O.; Zhuravlev, A.; Kochemazov, S.; Vatutin, E..(2016}).On the Construction of Triples of Diagonal Latin Squares of Order 10. Electronic Notes in Discrete Mathematics. pp. 307–312. DOI: 10.1016/j.endm.2016.09.053.[27]
- "Diagonalization and Canonization of Latin Squares". In:.(2023}).Supercomputing (RuSCDays 2023). Springer, Cham. pp. 48–61.(LNCS, vol. 14389).[28]
- "Completion of the Spectrum of Orthogonal Diagonal Latin Squares". In:.(1992}).Lecture Notes in Pure and Applied Mathematics. Marcel Dekker. pp. 43–49. — The foundational 1992 paper establishing the very first orthogonal pairs of DLS of order 10.[29]
Participating
To contribute computing power to ODLK1, download and install BOINC and attach to the project at:
There is no GPU requirement. Tasks run on idle CPU time and typically complete in well under an hour. Both Windows and Linux are fully supported; FreeBSD builds and an ARM64 Linux build for odlk3@home are also available, making the project compatible with single-board computers such as the Raspberry Pi 4 and later.
Participants may also join a team to compete on the credit leaderboards, or — if they run BOINC for multiple projects — use Gridcoin to earn cryptocurrency rewards for their combined contribution, as the project is whitelisted on the Gridcoin network.[30]
Statistics for ODLK1 are tracked on external aggregators including BOINCstats, Free-DC, and Formula BOINC.[31]
See also
External links
References
- ↑ Latin square. Wikipedia. Retrieved 2026-05-22}.
- ↑ Latin square – Orthogonality. Wikipedia. Retrieved 2026-05-22}.
- ↑ Latin square. Wikipedia. Retrieved 2026-05-22}.
- ↑ "Completion of the Spectrum of Orthogonal Diagonal Latin Squares". In:.(1992}).Lecture Notes in Pure and Applied Mathematics. Marcel Dekker. pp. 43–49.
- ↑ (2017-11-28}).New Project: ODLK1 [Latin Squares]. Overclock.net. Retrieved 2026-05-22}.
- ↑ (2017-09-11}).Thread: BOINC project ODLK. BOINC message boards. Retrieved 2026-05-22}.
- ↑ Message boards – News – ОДЛК. Retrieved 2026-05-22}.
- ↑ Message boards – Полная БД КФ ОДЛК 2017–2021. Retrieved 2026-05-22}.
- ↑ (2017-12-07}).Thread: BOINC project ODLK. BOINC message boards. Retrieved 2026-05-22}.
- ↑ Applications – ODLK1. Retrieved 2026-05-22}.
- ↑ Applications – ODLK1. Retrieved 2026-05-22}.
- ↑ News archive – ОДЛК. Retrieved 2026-05-22}.
- ↑ ODLK1 – User of the Day / News. Retrieved 2026-05-22}.
- ↑ T. Brada Experimental Grid – news. Retrieved 2026-05-22}.
- ↑ T. Brada Experimental Grid. Retrieved 2026-05-22}.
- ↑ Project status – ODLK1. Retrieved 2026-05-22}.
- ↑ Applications – ODLK1. Retrieved 2026-05-22}.
- ↑ (2026-05-22}).Project status – ODLK1. Retrieved 2026-05-22}.
- ↑ A287695 – OEIS. Retrieved 2026-05-22}.
- ↑ Top teams – ODLK1. Retrieved 2026-05-22}.
- ↑ Gridcoin – Rewarding Scientific Distributed Computing. Retrieved 2026-05-22}.
- ↑ Top participants – ODLK1. Retrieved 2026-05-22}.
- ↑ Using Volunteer Computing to Study Some Features of Diagonal Latin Squares. Retrieved 2026-05-22}.
- ↑ Applying Volunteer and Parallel Computing for Enumerating DLS of Order 9. Retrieved 2026-05-22}.
- ↑ Enumeration of Isotopy Classes of DLS. Retrieved 2026-05-22}.
- ↑ Evaluation of Efficiency… Order 10. Retrieved 2026-05-22}.
- ↑ On the Construction of Triples of DLS of Order 10. Retrieved 2026-05-22}.
- ↑ A287648 – OEIS (references). Retrieved 2026-05-22}.
- ↑ New Project: ODLK1 – project background. Overclock.net. Retrieved 2026-05-22}.
- ↑ Gridcoin – Rewarding Scientific Distributed Computing. Retrieved 2026-05-22}.
- ↑ Credit statistics – ODLK1. Retrieved 2026-05-22}.