Lists of small lattices and posets

Question

Does any one know where I can find a table that lists, up to isomorphism, all the lattices for a set with small order? and the same thing for how many posets can be formed from a set with small order. I have spent an hour trying to find such a table online but with no avail. Thanks in advance.

Answer 1

Late to the party, but if you need larger listings:

Lattices: Available for $ \le 16$ elements here, by V. Gebhardt and S. Tawn. With $n=16$ the count is $1\,471\,613\,387$. In fact they have listed lattices of up to 20 elements but for $n>16$ the listings are inconveniently large to publish.

Posets: Available for $n \le 10$ elements here, by B. McKay. With $n=10$ the count is $2\,567\,284$. If you need more, you can use a C program by B. McKay and G. Brinkmann's to list them yourself. One version of their poset-listing program is available here (yes, it's an arcane location).

For very small orders you can just use SageMath's "Posets(n)", but it is quite inefficient for $n \ge 8$, unless they have improved the algorithm in a later version.