Let l>=1 be an arbitrary odd integer and p,q and r primes. We show that there
exist infinitely many ternary cyclotomic polynomials \Phi_{pqr}(x) with
l^2+3l+5<= p<q<r such that the set of coefficients of each of them consists of
the p integers in the interval [-(p-l-2)/2,(p+l+2)/2]. It is known that no
larger coefficient range is possible. The Beiter conjecture states that the
cyclotomic coefficients a_{pqr}(k) of \Phi_{pqr} satisfy |a_{pqr}(k)|<= (p+1)/2
and thus the above family contradicts the Beiter conjecture. The two already
known families of ternary cyclotomic polynomials with an optimally large set of
coefficients (found by G. Bachman) satisfy the Beiter conjecture.Comment: 20 pages, 7 Table
