Generating checkboxes in Rails 4

I want to generate some checkboxes depending on select value. So i have select tag:

<%= f.collection_select :type, RequestType.order(:typeName), :id, :typeName,
 {include_blank:true }, {:class => "types"} %>

When the value of select changes i want to generate some checkboxes, for that i have div:

<div id="sub_types"> </div>

where i want to generate my checkboxes

def show_sub_types
        @rtype = params[:id];
        @stypes = RequestSubType.where("request_type_id=?", @rtype).all
         respond_to do |format|
         format.js
         format.html
        end
end

My method grabs all subtypes and passes them to js file show_sub_types.js.erb

$("#sub_types").html("");
$("#sub_types").append("<%= j render 'show_sub_types', stypes: @stypes %>");

In my js file i render partial show_sub_types.html.erb in which i want to generate my checkboxes:

<% stypes.each do |type| %>
        <%= check_box_tag "subtype", type.id %>
        <%= type.subTypeName %>
        <br>
<% end %>

In my partial i do something like this. This code generate me my checkboxes. They look like that:

<input type="checkbox" name="subtype" id="subtype" value="1">

But now i don't know how to submit these checkbox values with my form.I want to store multiple checkbox values in db as array.