Summary: A set of $k$ integers is a 2-basis if every positive integer up to $n$ can be expressed as the sum of no more than 2 values from the set; an extremal 2-basis is one for which $n$ is as large as possible. A new algorithm extends the lower bound of Mossige for symmetric bases. An assumed modulo structure is combined with local search. These 2-bases match all known extremal values for $k$ from 11 to 20. Bases out to $k = 82$ are given.

11B13

h-basis, extremal h-basis