2 new combinatorial structures from DLS of order 9 was found in the projects Gerasim@Home and RakeSearch:

* 19N52M19C — 012345678123480567681753420748561032504672813837206145270814356456037281365128704
* 25N58M25C — 012345678120487365308561742547632081674158230786023154851276403235704816463810527

Traversed 23.96% of the search space, 23947 ODLS CFs of order 9 found at this moment.

The post-processing has been changed in such a way that now the found ODLS CFs are laid out by lines and the xSODLS number is calculated (see screenshot). At the moment all 88 DSODLS CFs  have been found (it is interesting if the results obtained earlier are correct or not yet? :), 108 SODLS CFs of 470 known ones and 3713 ESODLS CFs found.

Each partial loop is a loop in a diagonal Latin square by definition. Similarly, by definition, each intercalate is a partial loop of length 4. These simple statements allow us to establish a number of relationships between the values of the numerical series associated with loops and intercalates and calculated earlier:

1. For loops: 0 <= A307166(n) <= A307167(n).
2. For partial loops: 0 <= A307170(n) <= A307171(n).
3. For minimum values: 0 <= A307163(n) <= A307170(n) <= A307166(n).
4. For maximum values: A307164(n) <= A307171(n) <= A307167(n).

Add to OEIS, the first swallow (https://oeis.org/draft/A307163) went, or rather, flew :)