# Rates of the Codes in MinT

This page shows plots of the information rate ρ := n/s and the relative minimum distance δ := d/s of all [s,n,d]-codes known by the MinT database.

For each code the chart contains a single point with coordinates (δ,ρ). If the length s of the code is larger than the largest codimension considered by MinT for this base b, the point is black. If its length is smaller, its color is blue, with brighter colors uses for codes with smaller length.

Different background colors are used for regions that are asymptotically (i.e., for large s) unreachable due to different bounds:

 Asymptotic Singleton bound Asymptotic Hamming bound Asymptotic Plotkin bound Asymptotic Bassalygo–Elias bound Asymptotic McEliece–Rodemich–Rumsey–Welch bound

The asymptotic Gilbert–Varšamov bound is ploted as a green curve, the asymptotic Tsfasman–Vlăduţ–Zink bound (for square bases greater or equal 9) as a blue line. For b ≥ 49 the latter exceeds the first one in a certain region. For points on or below these curves arbitrarily long codes exist.

## For b = 2

Points are black for length s > 260.

## For b = 3

Points are black for length s > 250.

## For b = 4

Points are black for length s > 260.

## For b = 5

Points are black for length s > 150.

## For b = 7

Points are black for length s > 110.

## For b = 8

Points are black for length s > 173.

## For b = 9

Points are black for length s > 150.

## For b = 16

Points are black for length s > 130.

## For b = 25

Points are black for length s > 110.

## For b = 27

Points are black for length s > 110.

## For b = 32

Points are black for length s > 110.

## For b = 49

Points are black for length s > 55.

## For b = 64

Points are black for length s > 91.

## For b = 81

Points are black for length s > 82.

## For b = 128

Points are black for length s > 78.

## For b = 256

Points are black for length s > 68.