How can a scientist get a more accurate
estimate using quadrat samping?

Estimate should maximize both precision and accuracy. In everyday English we often use these terms interchangeably, but in science, they have different meanings. Accuracy refers to how close to the true mean (μ) our estimate is. That is, if we somehow could know the true number of slugs residing on Mt. Moosilauke we could compare our estimate to it and find out how accurate we are. Obviously, we would like our estimate to be as close to the true value as possible.
In addition, we would like to avoid any bias in our estimate. An estimate would be biased if it consistently over- or under-estimated the true mean. Bias may arise in many ways, but one frequent source is by the selection of sample plots that are nonrandom with respect to the abundance of the target organism. For example, if we looked for slugs at Moosilauke only in sunny, dry open fields, our estimate would probably be much lower than the true abundance. (Hope this helps)

Ihaven't done that yet, so no idea,but this is not the right place to ask