Max dimension of a lattice

[N. J. A. Sloane]

In his 1992 book "Combinatorics and Partially Ordered Sets",
Tom Trotter mentions a 1984 question from Sands,
What is the max dimension of a lattice having n elements?

I won't repeat the definition since it is complicated.

But does anyone know if the first few terms have been computed?

He gives references to papers by Ganter et al., Furedi and Kahn, Sali,
so there is a fair amount of literature.

NJAS

PS
A week or two ago I asked if someone could compute the next term of
%S A001289 1,2,3,8,48,150357
%N A001289 Number of equivalence classes of Boolean functions modulo linear functions

Since then I have heard that a(7) was computed 10 years ago, so the sequence now reads:

%S A001289 1,2,3,8,48,150357,63379147320777408548
...
%D A001289 Xiang-Dong Hou, AGL(m,2) acting on R(r,m)/R(s,m), J. Algebra, 171 (1995), 
921-938.
...