A Hales-Jewett set is a set of words of a given length on a specified alphabet
with the property that whenever it is 2-colored, there must be a monochromatic
combinatorial line. We show that any Hales-Jewett set consisting of length 4 words
on the alphabet {1, 2, 3} must have at least 25 members and produce an example of a
minimal Hales-Jewett set with 37 members.