Shadow on pure white - three.js

Question

I'm trying to create a pure white scene where the only hint of depth is by moving a spotLight around with your mouse. I like the effect I have now but I was wondering how I could get the entire field (now gray) to be pure white, while keeping the shadow.
If I turn ambient light up I lose the shadow.
camera = new THREE.PerspectiveCamera( 35, window.innerWidth / window.innerHeight, 1, 1000 );
camera.position.set( 0, 50, 0 );
var controls = new OrbitControls( camera, renderer.domElement );
controls.addEventListener( 'change', render );
controls.minDistance = 20;
controls.maxDistance = 500;
controls.enablePan = false;
var ambient = new THREE.AmbientLight( 0xffffff, .7 );
scene.add( ambient );
spotLight = new THREE.SpotLight( 0xffffff, 1 );
spotLight.position.set( 0, 10, 0 );
spotLight.target.position.set( 0, 0, 0 );
spotLight.angle = 1.05;
spotLight.penumbra = 0.05;
spotLight.decay = 1;
spotLight.distance = 200;
spotLight.castShadow = true;
spotLight.shadow.mapSize.width = 1024;
spotLight.shadow.mapSize.height = 1024;
spotLight.shadow.camera.near = 10;
spotLight.shadow.camera.far = 200;
scene.add( spotLight );
lightHelper = new THREE.SpotLightHelper( spotLight );
// scene.add( lightHelper );
shadowCameraHelper = new THREE.CameraHelper( spotLight.shadow.camera );
// scene.add( shadowCameraHelper );
// scene.add( new THREE.AxisHelper( 10 ) );
var material = new THREE.MeshPhongMaterial( { color: 0xffffff, dithering: true } );
var geometry = new THREE.BoxGeometry( 2000, 1, 2000 );
var mesh = new THREE.Mesh( geometry, material );
mesh.position.set( 0, - 1, 0 );
mesh.receiveShadow = true;
scene.add( mesh );
var material = new THREE.MeshPhongMaterial( { color: 0xffffff, dithering: true } );
geometry = new THREE.BoxGeometry( 3, 1, 2 );
var mesh = new THREE.Mesh( geometry, material );
mesh.position.set( 0, 0, 0 );
mesh.castShadow = true;
scene.add( mesh );