  In 1998, Khodkar showed that the minimal critical set in the Latin square
corresponding to the elementary abelian 2-group of order 16 is of size at most
124. Since the paper was published, improved methods for solving integer
programming problems have been developed. Here we give an example of a critical
set of size 121 in this Latin square, found through such methods. We also give
a new upper bound on the size of critical sets of minimal size for the
elementary abelian 2-group of order $2^n$: $4^{n}-3^{n}+4-2^{n}-2^{n-2}$. We
speculate about possible lower bounds for this value, given some other results
for the elementary abelian 2-groups of orders 32 and 64. An example of a
critical set of size 29 in the Latin square corresponding to the elementary
abelian 3-group of order 9 is given, and it is shown that any such critical set
must be of size at least 24, improving the bound of 21 given by Donovan,
Cooper, Nott and Seberry.
