Line-by-line scanning with linear arrays is a standard image formation method in clinical ultrasound. This method examines progressively a given region of interest by conducting focused pulse-echo measurements with dynamic transmit and receive apertures. Such apertures widen with the focal length as a function of a given F-number and improve the image quality by extending the depth of field (DOF) and suppressing grating lobes. Fixed F-numbers, however, limit the lateral resolution. Herein, frequency dependence of the F-number is incorporated into both the transmit and the receive focusing to widen the apertures for low frequencies and improve the lateral resolution. Frequency-dependent transmit and receive F-numbers are proposed. These F-numbers, which can be expressed in closed form, maximize the lateral resolution under constraints on the DOF and the grating lobes. A phantom experiment showed that the proposed F-numbers eliminate grating lobe artifacts and improve both image uniformity and contrast to a similar extent as fixed F-numbers. These metrics, compared to the usage of the full apertures, improved by up to 14.1 % and 8.3 %, respectively. The proposed F-numbers, however, improved the lateral resolution by up to 24 % compared to the fixed F-numbers.