A technological improvement is generally considered to be an advancement or innovation that enhances efficiency, productivity, or capability through the use of technology. Among the options you provided, the following would constitute a technological improvement:
The discovery of a way to improve software speed that increases employee productivity.
This option directly relates to enhancing the technology used (software speed) which leads to better productivity, making it a clear example of technological improvement.
The other options, while potentially beneficial for productivity or competitiveness, do not specifically involve a technological advancement.