This paper studies the quantity p(n,r), that is the minimal number of edges of an n-uniform hypergraph without panchromatic coloring (it means that every edge meets every color) in r colors. If [Formula presented] then all bounds have a type [Formula presented], where A₁, A₂ are some algebraic fractions. The main result is a new lower bound on p(n,r) when r is at least cn; we improve an upper bound on p(n,r) if n=o(r^3∕2). Also we show that p(n,r) has upper and lower bounds depending only on n∕r when the ratio n∕r is small, which cannot be reached by the previous probabilistic machinery. Finally we construct an explicit example of a hypergraph without panchromatic coloring and with [Formula presented].