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 (\tau+1) time units, under a strict decoding-delay constraint \tau. 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\geq\tau+b-a is a prime power. In this work, we present an explicit rate-optimal streaming code, for all possible \{a, b,\tau\} parameters, over a field of size q^{2} for prime power q\geq \tau. This is the smallest-known field size of a general explicit rate-optimal construction that covers all \{a, b, \tau\} 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. © 2021 IEEE.