diff --git a/Project.toml b/Project.toml
index bd7af42..431c176 100644
--- a/Project.toml
+++ b/Project.toml
@@ -4,11 +4,13 @@ authors = ["Ritter.Marc <Ritter.Marc@physik.uni-muenchen.de>, Hiroshi Shinaoka <
 version = "0.9.15"
 
 [deps]
+BitIntegers = "c3b6d118-76ef-56ca-8cc7-ebb389d030a1"
 EllipsisNotation = "da5c29d0-fa7d-589e-88eb-ea29b0a81949"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 QuadGK = "1fd47b50-473d-5c70-9696-f719f8f3bcdc"
 
 [compat]
+BitIntegers = "0.3.5"
 EllipsisNotation = "1"
 QuadGK = "2.9"
 julia = "1.6"
diff --git a/src/TensorCrossInterpolation.jl b/src/TensorCrossInterpolation.jl
index 4040107..4920c0b 100644
--- a/src/TensorCrossInterpolation.jl
+++ b/src/TensorCrossInterpolation.jl
@@ -2,6 +2,7 @@ module TensorCrossInterpolation
 
 using LinearAlgebra
 using EllipsisNotation
+using BitIntegers
 import QuadGK
 
 # To add a method for rank(tci)
diff --git a/src/cachedfunction.jl b/src/cachedfunction.jl
index a5f8aef..49f9a6a 100644
--- a/src/cachedfunction.jl
+++ b/src/cachedfunction.jl
@@ -5,7 +5,7 @@ function using the usual function call syntax.
 The type `K` denotes the type of the keys used to cache function values, which could be an integer type. This defaults to `UInt128`. A safer but slower alternative is `BigInt`, which is better suited for functions with a large number of arguments.
 `CachedFunction` does not support batch evaluation of function values.
 """
-struct CachedFunction{ValueType,K<:Union{UInt32,UInt64,UInt128,BigInt}} <: BatchEvaluator{ValueType}
+struct CachedFunction{ValueType,K<:Union{UInt32,UInt64,UInt128,BigInt,BitIntegers.AbstractBitUnsigned}} <: BatchEvaluator{ValueType}
     f::Function
     localdims::Vector{Int}
     cache::Dict{K,ValueType}
@@ -15,8 +15,11 @@ struct CachedFunction{ValueType,K<:Union{UInt32,UInt64,UInt128,BigInt}} <: Batch
         for n in 2:length(localdims)
             coeffs[n] = localdims[n-1] * coeffs[n-1]
         end
+        if K == BigInt
+            @warn "Using BigInt for keys. This is SUPER slower and uses more memory. The use of BigInt is kept only for compatibility with older code. Use BitIntegers.UInt256 or bigger integer types with fixed size instead."
+        end
         if K != BigInt
-            sum(coeffs .* (localdims .- 1)) < typemax(K) || error("Too many dimensions. Use BigInt instead of UInt128.")
+            sum(coeffs .* (localdims .- 1)) < typemax(K) || error("Overflow in CachedFunction. Use ValueType = a bigger type with fixed size, e.g., BitIntegers.UInt256")
         end
         new(f, localdims, cache, coeffs)
     end
diff --git a/test/test_cachedfunction.jl b/test/test_cachedfunction.jl
index 366d243..c52a830 100644
--- a/test/test_cachedfunction.jl
+++ b/test/test_cachedfunction.jl
@@ -1,7 +1,7 @@
 using Test
 import TensorCrossInterpolation as TCI
 import TensorCrossInterpolation: BatchEvaluator, MultiIndex
-
+import BitIntegers
 struct TestF <: TCI.BatchEvaluator{Float64}
 end
 
@@ -96,7 +96,7 @@ end
         f(x) = 1.0
         nint = 4
         N = 64 * nint
-        cf = TCI.CachedFunction{Float64,BigInt}(f, fill(2, N))
+        cf = TCI.CachedFunction{Float64,BitIntegers.UInt512}(f, fill(2, N))
         x = ones(Int, N)
         @test cf(x) == 1.0
         @test TCI._key(cf, x) == 0