# Input and output files for Hurwitz classes

The links below lead to NETmap input and output files for exactly one representative from every modular group Hurwitz class of NET maps through degree 30. This information is organized first according to elementary divisors m and n. There is one web page of links for each choice of m and n with the product mn at least 2 and at most 30. For three of the classes, class 2 for m=2 and n=1, and classes 9 and 10 for m=2 and n=2, the maps have only three postcritical points for each choice of the translation vector and so don't give any NET maps.

Here is how the entries for a given ordered pair (m,n) are ordered. We use the fact that modular group Hurwitz classes of NET maps are classified by equivalence classes of Hurwitz structure sets. These Hurwitz structure sets are disjoint unions of four subsets of the form {±(α,β)} with (α,β) ∈ ℤ2m ⊕ ℤ2n. We represent α and β by nonnegative integers a and b. We define an ordering ≤ on ordered pairs of nonnegative integers so that (a,b) ≤ (c,d) if and only if either b<d or b=d and a≤c. This ordering of ordered pairs leads to an ordering of sets of four signed ordered pairs. This determines the ordering of the entries for (m,n). So the first entry always has structure set {(0,0),±(1,0),±(2,0),±(3,0)} except when m=2 ((1,0)=-(3,0) in ℤ2m ⊕ ℤ2n when m=2).

There are 46,245 Hurwitz classes of NET maps with degree at most 30.
• There are 4 equivalence classes with degree 2.
• There are 9 equivalence classes with degree 3.
• There are 34 equivalence classes with degree 4; 24 of these have m=4 and n=1 and 10 of these have m=2 and n=2.
• There are 25 equivalence classes with degree 5.
• There are 88 equivalence classes with degree 6.
• There are 47 equivalence classes with degree 7.
• There are 218 equivalence classes with degree 8; 133 of these have m=8 and n=1 and 85 of these have m=4 and n=2.
• There are 163 equivalence classes with degree 9; 120 of these have m=9 and n=1 and 43 of these have m=3 and n=3.
• There are 269 equivalence classes with degree 10.
• There are 140 equivalence classes with degree 11.
• There are 819 equivalence classes with degree 12; 618 of these have m=12 and n=1 and 201 of these have m=6 and n=2.
• There are 228 equivalence classes with degree 13.
• There are 583 equivalence classes with degree 14.
• There are 646 equivalence classes with degree 15.
• There are 1447 equivalence classes with degree 16; 789 of these have m=16 and n=1, 503 of these have m=8 and n=2, and 155 of these have m=4 and n=4.
• There are 469 equivalence classes with degree 17.
• There are 2,001 equivalence classes with degree 18; 1,544 of these have m=18 and n=1 and 457 of these have m=6 and n=3.
• There are 629 equivalence classes with degree 19.
• There are 2,556 equivalence classes with degree 20; 1,935 of these have m=20 and n=1 and 621 of these have m=10 and n=2.
• There are 1,505 equivalence classes with degree 21.
• There are 1,902 equivalence classes with degree 22.
• There are 1,079 equivalence classes with degree 23.
• There are 6,250 equivalence classes with degree 24; 3,976 of these have m=24 and n=1 and 2,284 of these have m=12 and n=2.
• There are 2,010 equivalence classes with degree 25; 1,678 of these have m=25 and n=1 and 332 of these have m=5 and n=5.
• There are 3,037 equivalence classes with degree 26.
• There are 3,594 equivalence classes with degree 27; 2,562 of these have m=27 and n=1 and 1,032 of these have m=9 and n=3.
• There are 5,856 equivalence classes with degree 28; 4,472 of these have m=28 and n=1 and 1,384 of these have m=14 and n=2.
• There are 2,116 equivalence classes with degree 29.
• There are 8,521 equivalence classes with degree 30.