Streaming codes are a class of packet-level erasure codes that ensure packet recovery over a sliding window channel which allows either a burst erasure of size b or a random erasures within any window of size (τ + 1) time units, under a strict decoding-delay constraint τ . The field size over which streaming codes are constructed is an important factor determining the complexity of implementation. The best known explicit rate-optimal streaming code requires a field size of q 2 where q ≥ τ + b − a is a prime power. In this work, we present an explicit rate-optimal streaming code, for all possible {a, b, τ } parameters, over a field of size q 2 for prime power q ≥ τ . This is the smallest-known field size of a general explicit rate-optimal construction that covers all {a, b, τ } parameter sets. We achieve this by modifying the non-explicit code construction due to Krishnan et al. to make it explicit, without change in field size.