How to create a custom Tile-Map with its own extent in OpenLayers 3?

Question

I am a newbie to Openlayers and currently dealing with a problem in setting up a custom tile-map. I have a base tile at zoom = 0 as png which has an extent of 56 by 56 kilometres and a resolution of 218.75 meters. Currently the tile-archive goes down to zoom-level 4. I used the projection in EPSG:25833 in proj4 and displayed the tiles via ol.source.xyz. I defined extent and resolution. However the map is not displayed at the correct coordinates. On loading it jumps to a higher zoom-level than entered and displays a small part of a tile. When zooming out the defined extent is just a small rectangle in the center of the map and coordinates go up to exorbitant numers around this extent.

I searched in stackexchange an in the OL-Apidoc, but could not find my error.

Here is my current code:

proj4.defs('EPSG:25833', '+proj=utm +zone=33 +ellps=WGS84 +datum=WGS84  +units=m +no_defs');
var projection25833 = ol.proj.get("EPSG:25833");

var tileLayer = new ol.layer.Tile({
    source: new ol.source.XYZ({
        projection: projection25833,
        url: "{z}/{x}/{-y}.png",
        extent: [364900,5791100,420900,5847100],
        tileSize: [256, 256],
        minZoom: 0,
        maxZoom: 4
    })
});

var myView = new ol.View({
    projection: projection25833,
    extent: [364900,5791100,420900,5847100],
    center: [392900, 5819100],
    resolution: 218.75,
    zoom: 0,
    minZoom: 0,
    maxZoom: 4
});

var map = new ol.Map({
    target: "mapDIV",
    layers: [tileLayer],
    view: myView
});

Answer 1

I obviously found an own solution for this problem. Because OL by default uses its own zoom-levels, "0" means a global view. I had to define a custom projection with the given extent to fix this problem:

var projection25833bln = new ol.proj.Projection({
    code: "EPSG:25833bln",
    global: false,
    extent: [364900,5791100,420900,5847100]
});

The question remains whether I still need proj4 for eventually transforming WGS84-coordinates into UTM or vice versa.