  In this work, we revisit some combinatorial and information-theoretic
extension techniques for detecting non-algebraic matroids. These are the
Dress-Lov\'asz and Ahlswede-K\"orner extension properties. We provide
optimizations of these techniques to reduce their computational complexity,
finding new non-algebraic matroids on 9 and 10 points. In addition, we use the
Ahlswede-K\"orner extension property to find better lower bounds on the
information ratio of secret sharing schemes for ports of non-algebraic
matroids.
