  Let $N \geq2$ and let $1 < a_1 < ... < a_N$ be relatively prime integers.
Frobenius number of this $N$-tuple is defined to be the largest positive
integer that cannot be expressed as $\sum_{i=1}^N a_i x_i$ where $x_1,...,x_N$
are non-negative integers. The condition that $gcd(a_1,...,a_N)=1$ implies that
such number exists. The general problem of determining the Frobenius number
given $N$ and $a_1,...,a_N$ is NP-hard, but there has been a number of
different bounds on the Frobenius number produced by various authors. We use
techniques from the geometry of numbers to produce a new bound, relating
Frobenius number to the covering radius of the null-lattice of this $N$-tuple.
Our bound is particularly interesting in the case when this lattice has equal
successive minima, which, as we prove, happens infinitely often.
