New nonbinary code bounds based on divisibility arguments.

For  q , n , d ∈ N , let  A q ( n , d ) be the maximum size of a code  C ⊆ [ q ] n with minimum distance at least d. We give a divisibility argument resulting in the new upper bounds  A 5 ( 8 , 6 ) ≤ 65 , A 4 ( 11 , 8 ) ≤ 60 and  A 3 ( 16 , 11 ) ≤ 29 . These in turn imply the new upper bounds  A 5 ( 9 , 6 ) ≤ 325 ,  A 5 ( 10 , 6 ) ≤ 1625 ,  A 5 ( 11 , 6 ) ≤ 8125 and  A 4 ( 12 , 8 ) ≤ 240 . Furthermore, we prove that for  μ , q ∈ N , there is a 1-1-correspondence between symmetric  ( μ , q ) -nets (which are certain designs) and codes  C ⊆ [ q ] μ q of size  μ q 2 with minimum distance at least  μ q - μ . We derive the new upper bounds  A 4 ( 9 , 6 ) ≤ 120 and  A 4 ( 10 , 6 ) ≤ 480 from these 'symmetric net' codes.