A lower bound for positive cubature formulae on the unit ball is given. For the Chebyshev weight function on the ball in ℝ2, the new bound shows that a positive cubature formula of degree s with all nodes inside the ball will need at least Ns≥ 0.13622s2(1 + O(s-1)) number of nodes, in comparison with the classical lower bound of Ns≥0.125s2(1 + O (s-1)). © 2003 Elsevier Science (USA). All rights reserved.
Xu, Y. (2003). Lower bound for the number of nodes of cubature formulae on the unit ball. Journal of Complexity, 19(3), 392–402. https://doi.org/10.1016/S0885-064X(03)00007-4