The uniform matroid 
is the matroid on an 
-element ground set whose independent
sets are exactly the subsets of
size at most 
,
where 
.
Its matroid rank is 
, and its matroid bases are
all the 
-element
subsets. In particular it has 
matroid bases.
A parallel 
-thickening
replaces each ground set element by a parallel class
of 
elements. Chen et al. (2026) proved that every such thickening of 
with 
and 
satisfies the multiplicative Merino-Welsh
conjecture. For 
,
they found that 62 is the smallest number of elements in a counterexample within
this family, attained by doubling each element of 
. This minimum is not asserted over all matroids.
