Parallel-Class Splitting and Constructive Lower Bounds for the Social Golfer Problem

We establish constructive lower bounds for the Social Golfer Problem using resolvable designs and explicit schedules. We show that, for p≥2, any index-one RTD(p,2p-1) can have one parallel class replaced by two compatible classes, yielding W(2p-1,p)≥2p. In particular, this holds whenever 2p-1 is a prime power. Given an RTD(p,2p), the same replacement works when the number of groups is g=2p, although the resulting lower bound already follows from standard group filling. We also derive a ten-round schedule for groups of five on 50 players by completing a partial class of Brouwer's ITD(10,2;6) with two hole transversals. Finally, cyclic difference arrays or complete schedules establish W(20,7)≥15, W(21,7)≥16, W(28,7)≥21, and W(14,13)≥6. No exactness or optimality claim is made. The record includes the manuscript, LaTeX source, and supplementary schedules with a standalone Python validator. AI assistance in the research and manuscript drafting is disclosed in the paper. Licenses: the manuscript, LaTeX sources, schedules and original numerical tables are CC BY 4.0. The supplementary Python validator is MIT. These licenses apply to separate components; see LICENSES.txt.