How can I store boolean array of size 3000 efficiently in milvus?

I have a boolean array which represents store-availability of retail products across 3000 different stores.

so, my schema looks like below:

product_id = FieldSchema(
    name="product_id", 
    dtype=DataType.INT64, 
    is_primary=True,
    auto_id=False
)

product_title_vector = FieldSchema(
    name="product_title_vector", 
    dtype=DataType.FLOAT_VECTOR,
    dim=768,
)

store_availability = FieldSchema(
    name="store_availability", 
    dtype=DataType.ARRAY, 
    element_type=DataType.BOOL,
    max_capacity=3000
)

The catch here is as per the general rule, boolean array of size 3000 will take ~3KB per record.

I have 5 million items/records. so in total store_availability field alone will take 15GB as per the below calculation.

memory = 3000 bytes/item * 5,000,000 items = 15GB

And then I perform a milvus search with expr for filtering results based on given store-id like below:

query_vector = np.random.random((1, 128)).astype(np.float32)
query_vector_resized = np.resize(query_vector, (1, 768))

store_id = 1

filter_expr = "store_availability[{}] == true".format(store_id - 1)
print("Filter Expression : ", filter_expr)

search_params = {"metric_type": "L2", "params": {"nprobe": 16}}
search_results = collection.search(
    data=query_vector_resized,
    anns_field="product_title_vector",
    expr=filter_expr,
    param=search_params,
    limit=1
    
)

I am finding this 15GB for a single metadata field as resource-intensive. Although it is better performant, what if the number of stores increase to 40,000 in future.

I tried sparse-vector representation but most of the products are available on 80% of the stores and still it consumes a lot of space.

Any approaches that can be suggested for making this space-efficient while having filter-expr within search will be of great help!