Maximum number of distinct substrings

Pyth, 12 bytes

l.Ml{.:Z)^UE

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Pure brute force.

Explanation

• Implicit: append Q to the program.
• Implicit: read and evaluate a line of input (n) in Q.
• E: read and evaluate a line of input (k).
• U: get a range [0, ..., k-1].
• ^: get all n-length strings of [0, ..., k-1].
• .M: find the ones that give a maximum for function f(Z):
  • .:Z: find the substrings of Z
  • {: remove duplicates
  • l: get the number of unique substrings
• l: get the number of such strings

Jelly, 9 bytes

ṗµẆQLµ€ML

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Input in reversed order. Brute force.

Mathematica, 96 bytes

Last[Last/@Tally[Length@Union@Flatten[Table[Partition[#,i,1],{i,s}],1]&/@Tuples[Range@#2,s=#]]]&