The set of increments of the Wiener process VT = {a^-1/2 [W(τ + a_T ·) - W(τ)]/L_T, 0 ≤ τ ≤ T - a_T}, where a_T ∈ (0, T) and L_T = (2 [log(T/a_T) + loglog T]^1/2 is considered. Under the assumption log(T/a_T)/loglog T → c, the set V_T oscillates between bK and K, where b = [c/(c + 1)^1/2 and K is the Strassen ball.