We present an infinite family of protocols to distill magic states for $T$-gates that has a low space overhead and uses an asymptotic number of input magic states to achieve a given target error that is conjectured to be optimal. The space overhead. defined as the ratio between the physical qubits to the number of output magic states. is asymptotically constant. https://macorners.shop/product-category/blue-bottle-lamp-gift-box/