A good set of benchmark matrices depends on the problem being solved (sparse solvers, eigenvalue problems, special structures, et cetera). Often, you'll want to include some real-life example applications of the algorithm that you are testing, or matrices that lead to particularly difficult problems to solve. Just choosing matrices at random won't cut that. Hence good sets of benchmarks mostly contain matrices that are carefully chosen, and are publication-worthy in themselves; some get lots of citations.
Among many of them, I shall mention here:
For new results, in integer multiplication, check the breakthrough paper by: David Harvey, and Joris Van Der Hoeven, et al . Integer multiplicaion in $O(n*(log$ $n))$. This proves Schonhage Strassens' conjecture from the 1970s that integer multiplication is really possible in $O(n*(log$ $n))$. From, straightforward (school) integer multiplication which is $O( n^{2}) $, to karatsubas' algorithm which is $O(n^{1.58})$, to $O(n*(log$ $n))$, by above authors. The authors use the property of specific multivariate polynomial rings that admit efficient multiplication.
The authors show that integer multiplication (which is one dimensional) could be represented in a setting of a specific multivariate polynomial ring. Starting with a binary representation of integers, begin with the fixed point coordinate vectors(to a precision), and then go on to utilize them in coefficient rings for that polynomial representation. One could select parameters, and reduce the integer multiplication problem to one of convolution over a ring with a specific structure, reaching the bound.
The bound is a significant improvement over earlier algorithms, and with many digits the efficiencies are apparent, for a large number of digits billions, and larger scales as author(s) claim its unknown, but good performance is possible.
Best Answer
Don't miss this wonderful post by Marsaglia. He's not a fan of the Mersenne Twister and offers some strong PRNGs with exceptionally small code footprints. One of his examples is: