Cardinality of Master Code

Theorem
Let $\map V {n, p}$ be a master code of length $n$ modulo $p$.

Then there are $p^n$ elements of $\map V {n, p}$.

Proof
For each term of a sequence in $\map V {n, p}$ there are $p$ possible values.

There are $n$ such terms.

Hence there are $\underbrace {p \times p \times \cdots \times p}_{n \text { times} } = p^n$ different possible sequences in $\map V {n, p}$.