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This paper is a continuation of the paper ‘Functions without short implicents. Part I: lower estimates of weights’. In Part II we propose various methods of construction of  n -place Boolean functions not admitting implicents of  k  variables. The first of the methods proposed is based on the gradient algorithm, the second and the third ones depend on a certain combinatorial principle of construction, while the fourth method is based on a random choice of elements in the function support. The above methods have different efficiency depending on the value of  k . We give upper estimates for the minimal value  w  ( n, k ) of weights of the so-constructed functions. Together with the lower estimates of  w  ( n, k ) from the first part of the paper this allows us to obtain an asymptotically sharp estimate  w  ( n, k ) = Θ (ln  n ) as  n  → ∞.

Functions without short implicents. Part II: Construction