Absolute maximum number of possible PN sequences for given length
No, that isn't possible. Think about it in the geometric sense, where each bit in the sequence is a dimension. In that context, you can recast your question as:


  In an $n$-dimensional space, are there any sets of $M$ vectors (where $M &gt; n$) that are mutually orthogonal?


For example, in three-dimensional space, can you construct a set of four vectors that are mutually orthogonal to one another? You can't. Stated in linear algebraic terms, you can only have as many basis vectors as the dimensionality of the space.