  In radio interferometry imaging, the gridding procedure of convolving
visibilities with a chosen gridding function is necessary to transform
visibility values into uniformly sampled grid points. We propose here a
parameterised family of "least-misfit gridding functions" which minimise an
upper bound on the difference between the DFT and FFT dirty images for a given
gridding support width and image cropping ratio. When compared with the widely
used spheroidal function with similar parameters, these provide more than 100
times better alias suppression and RMS misfit reduction over the usable dirty
map. We discuss how appropriate parameter selection and tabulation of these
functions allow for a balance between accuracy, computational cost and storage
size. Although it is possible to reduce the errors introduced in the gridding
or degridding process to the level of machine precision, accuracy comparable to
that achieved by CASA requires only a lookup table with 300 entries and a
support width of 3, allowing for a greatly reduced computation cost for a given
performance.
