  A Chebyshev-type quadrature for a given weight function is a quadrature
formula with equal weights. In this work we show that a method presented by
Kane may be used to produce tight bounds for the minimal number of nodes
required in Chebyshev-type quadratures for doubling weight functions. This
extends a long line of research on Chebyshev-type quadratures starting with the
1937 work of Bernstein.
