This paper investigates the ultimate accuracy of the NAND flash program algorithm that is determined by the statistical injection of electrons from the substrate to the floating gate. The granular nature of the electron flow during a constant-current Fowler-Nordheim program operation is shown to spread the programmed threshold-voltage distribution of the array cells. The electron injection statistics displays a Poissonian behavior for low amounts of transferred charge, but a sub-Poissonian character becomes clearly evident when large charge packets are stored. This effect is expected from the reduction of the tunnel oxide field that follows each electron storage event into the floating gate, establishing a correlation among such events. Finally, the impact of the electron injection statistical spread on the accuracy of the NAND flash program algorithm is investigated as a function of the technology node feature size, drawing projections on future NAND technologies.