Existence can be seen by an explicit construction of .
In for instance, Hardie et al. present an explicit construction of the map using poset models.
Thus we have a strongly explicit construction for a code that can be used to form a group testing matrix and so .
The correspondence is shown by an explicit construction of the *-representation from the state.
This method provides an explicit construction of the non-parametric sample, and makes clear the fact that the samples are discrete.
That all five actually exist is a separate question - one that can be answered easily by an explicit construction.
There is no known explicit construction producing an exponential lower bound.
Together with explicit constructions for lower dimensions (through 62), this leaves open only dimension 126.
An explicit construction is needed which is given as follows:
For classical Lie algebras there is a more explicit construction.