Tilemap Shader Glitch

I am working on a Unity shader that can display multiple different tiles on a single plane. Unity passes a floating point array to the shader with a list of tile IDs and a 16x16 tile map and for the most part it works perfectly, however there is one slight issue.

I have attached an image of the phenomenon, at the seams of the tiles you can see grey lines.

Below is the shader code:

 Shader "Unlit/TileMap"
 {
     Properties
     {
         // Texture configuration
         _DiffuseTex("Diffuse", 2D) = "white" {}
         _MaskTex("Mask", 2D) = "black" {}
         _MapWidth("Map Width", int) = 0
         _MaskMapWidth("Mask Mask Width", int) = 0
         _WorldWidth("World Width", int) = 0
 
 
         // Global illumination modifiers
         _GlobalLumosity("Global Lumosity", Range(0, 1)) = 1
         _GlobalHue("Global Hue", Color) = (1, 1, 1, 1)
 
     }
     SubShader
     {
         Tags { "Queue"="Transparent" "RenderType"="Transparent" }
         LOD 200
         ZWrite On
 
         Blend SrcAlpha OneMinusSrcAlpha
 
         Pass
         {
             CGPROGRAM
             #pragma target 4.0
             #pragma vertex vert
             #pragma fragment frag
             #include "UnityCG.cginc"
 
             struct appdata {
                 float4 vertex : POSITION;
                 float2 uv : TEXCOORD0;
             };
 
             struct v2f {
                 float2 uv : TEXCOORD0;
                 float4 vertex : SV_POSITION;
             };
 
             sampler2D _DiffuseTex;
             float4 _DiffuseTex_ST;
 
             sampler2D _MaskTex;
             float4 _MaskText_ST;
 
             uint _ID;
             uint _MapWidth;
             uint _MaskMapWidth;
             uint _WorldWidth;
 
             half _GlobalLumosity;
             float4 _GlobalHue;
 
             float _allIDs[16];
 
             v2f vert (appdata v) {
                 v2f o;
 
                 o.vertex = UnityObjectToClipPos(v.vertex);
                 o.uv = TRANSFORM_TEX(v.uv, _DiffuseTex);
 
                 return o;
             }
 
             fixed4 frag (v2f i) : SV_Target {
                 float mapSizeModif = 1.0f / _MapWidth;
                 float maskMapSizeModif = 1.0f / _MaskMapWidth;
                 float worldSizeModif = 1.0f / _WorldWidth;
 
                 // float lightness = tex2D (_MaskTex, i.uv * _MapWidth);
                 float lightness = 1.0f;
 
                 uint index = (int)  (floor(i.uv.x * _WorldWidth) +
                                     (floor(i.uv.y * _WorldWidth) * _WorldWidth));
 
                 i.uv.x = i.uv.x % worldSizeModif;
                 i.uv.y = i.uv.y % worldSizeModif;
 
                 uint id = (uint) _allIDs[index];
 
                 i.uv.x += mapSizeModif * (id % _MapWidth);
                 i.uv.y += mapSizeModif * floor (((float)id) / _MapWidth);
 
                 fixed4 col = tex2D (_DiffuseTex, i.uv);
                 col *= _GlobalLumosity;
                 col *= _GlobalHue;
 
                 col.a = lightness;
 
                 return col;
             }
 
             ENDCG
         }
     }
 }
 

And here is an image of what happens:

I feel like some sort of padding would be needed to fix this issue but I don't know what kind of padding I would need. I feel it has something to do with the lines, and an issue that involves some sort of floating point accuracy error:

// Convert position into localised scaling
i.uv.x = i.uv.x % worldSizeModif;
i.uv.y = i.uv.y % worldSizeModif;

And in fact, when I disable these lines it works perfectly - however obviously, the shader no longer displays the correct thing.

Any help would be appreciated!