The ideal sample size depends on the complexity of the underlying structure of the data (how many groups do you want to discriminate?), how variable the groups are and how well separated they are. Have you any prior data to based estimates of these on? If not, then you will be doing an exploratory study, interpreting the results as such (i.e. make no bold claims of discovery, rather use it to formulate hypotheses that can be falsified) and you can use the results to design a robust validation study.

Two basic issues:

1. The number of subjects must be much higher (at least five fold) than the number of variables. For this reason (and for other issues related to the well conditioning of discriminant analysis) I suggest you yo operate (before discriminant analysis) a principal component analysis and then operate discrimination using the main principal components as descriptors.

2. Subdivide your data set into a test and a training set. The model built on the training set will be then validated on the test set. Think of at least a 20% numerosity of test with respect to training set.

The attached paper is very useful to understand the problem of multiplicity of variables.

The above answer was relative to discriminat analysis (that is a supervised learning technique and thus can give rise to chance correlations). The Multidimensionale Scaling (or any other descriptive approaches like PCA) have no such limitations, clealry if you use too few subjects is hardly to generalize, but in principle you can work even with a number of subjects less than the number of variables, given you are only describing a data set without any inferential process (see attached PCA when subjects are less than variables).