How to shuffle eight items to approximate maximum entropy?

I need to analyze 8 chemical samples repeatedly over 5 days (each sample is analyzed exactly once every day). I'd like to generate pseudo-random sample sequences for each day which achieve the following:

• avoid bias in the daily sequence position (e.g., avoid some samples being processed mostly in the morning)
• avoid repeating sample pairs over different days (e.g. 12345678 on day 1 and 87654321 on day 2)
• generally randomize the distance between two given samples from one day to the other

I may have poorly phrased the conditions above, but the general idea is to minimize systematic effects like sample cross-contamination and/or analytical drift over each day. I could just shuffle each sequence randomly, but because the number of sequences generated is small (N=5 versus 40,320 possible combinations), I'm unlikely to approach something like maximum entropy.

Any ideas? I suspect this is a common problem in analytical science which has been solved, but I don't know where to look.