8 problems

Let $M(d,n)$ denote the set of Latin hypercubes of dimension $d$ and order $n$. A transversal is a set of $n$ entries containing each value in every coordinate position and each sy…

A latin hypercube of order $n$ and dimension $d$ is a $d$-dimensional array filled with $n$ symbols so that every line contains all symbols exactly once. A transversal is a diagona…

A latin $n$-cuboid of order $q$ is an $n$-dimensional array with one dimension of length less than $q$ and the remaining dimensions of length $q$, whose lines contain different sym…

For $d\in\mathbb N$, a $d$-dimensional order-$n$ Latin hypercube is a $d$-dimensional array indexed by $[n]^d$ with entries from $[n]$, such that every line contains each symbol ex…

A latin hypercube of dimension $d$ and order $n$ is a $d$-dimensional array filled with $n$ symbols so that every line contains all symbols exactly once. A near transversal is a co…

A latin hypercube of dimension $d$ and order $n$ is the $d$-dimensional analogue of a latin square, with every symbol occurring exactly once on each axis-parallel line. Sun's conje…

Let $Q^n(\mathbb{Z}_4)$ and $Q^n(\mathbb{Z}_2^2)$ denote the $n$-dimensional latin hypercubes isotopic to the Cayley tables of the corresponding iterated groups. A transversal is a…

Asymptotic enumeration conjecture.