A complete design is required and the form obtained with DOE is incomplete.
For example, this is an 8-factor, 4-level design table.
Thanks!

Do you mean a full factorial design, 8 factors each 4 Level? This means 4^8 Settings = 65536,
JMP does exactly this, see the script. BR
DOE(
Full Factorial Design,
{Add Response( Maximize, "Y", ., ., . ),
Add Factor( Continuous, {1, 2, 3, 4}, "X1", 0 ),
Add Factor( Continuous, {1, 2, 3, 4}, "X2", 0 ),
Add Factor( Continuous, {1, 2, 3, 4}, "X3", 0 ),
Add Factor( Continuous, {1, 2, 3, 4}, "X4", 0 ),
Add Factor( Continuous, {1, 2, 3, 4}, "X5", 0 ),
Add Factor( Continuous, {1, 2, 3, 4}, "X6", 0 ),
Add Factor( Continuous, {1, 2, 3, 4}, "X7", 0 ),
Add Factor( Continuous, {1, 2, 3, 4}, "X8", 0 ),
Make Design, Simulate Responses( 0 ), Set Run Order( Keep the Same ), Make Table
}
)
The result of this method is an exhaustive list of combinations.
4^8 = 65536

This is much more than the number of conformal Latin squares.
JMP does not directly create these designs using any of the DOE platforms. See this reference.
On the other hand, JMP produces very many useful designs. Perhaps another design would satisfy your need. Why do you require the orthomorphic Latin square design? Why will another design not satisfy your need?
I rewrote the sas code as VBA.
Can generate common orthogonal tables.

But when want to generate an orthogonal table of any factor, at any level, Get a repetition when it's not prime.