Appendix II

Appendix II. Creating  Latin squares of fixed order following the Sequential Enumeration scheme

1: start with order 4, write the first row  in standard format: 1 2 3 4

2: try to complete the Ls row by row and site by site (from left to right) by always choosing the lowest possible number for the subsequent sites

3; in case of failure return to the last site where you had a choice (the last-choice site) and took the lowest possible number

4; now take the lowest available number there and proceed, always taking lowest possible numbers

5; proceed in this manner, if in failure return to the last site where one or more choices are (still) available, always taking the lowest. If the process fails again return to the last but one choice site, etc.

6; proceed until the Ls is finished. Number it LS01

7; start the completion of LS02 by: taking the previously completed Ls as starting point, returning to the last choice site of that Ls, and following 5

8; proceed until there are no choice sites left in the previously completed LS.

“failure”: impossibility to meet the Latin square condition at a current site

“possible”: compatible with the Latin square condition

“available” possible and not yet adopted in a previous attempt to continue the process

“last” refers to the process in time of successively filling the sites, going from upper to lower rows, etc.


Our numbering of the  LS’s of order 4 and 5 (Chapters 2 and 3) follows the sequence of creation with the Sequential Enumeration scheme.