Computing almost minimal formulas on the square

The main purpose of this paper is to introduce a numerical method for the computation of cubature rules on the square [−1,1]2[−1,1]2 that are almost   minimal, i.e. with few points w.r.t. the degree of precision dd. In particular for all 24≤d≤5524≤d≤55 the sets {ξd}{ξd} and the weights {wk}{wk} are new. New rules are also achieved for degrees 15, d=17d=17, 19 and d=23d=23 respectively with 43, 54, 67 and 96 points.