An inverse-design framework is presented for linear dispersive water waves in bounded rectangular basins, exploiting the discrete transverse eigenmodes imposed by sidewall reflections as a synthesis basis. A transfer matrix mapping wavemaker inputs to free-surface elevation is constructed and inverted via regularisation to produce prescribed target fields on spatial ($x$-$y$), spatio-temporal ($y$-$t$), or volumetric ($x$-$y$-$t$) domains. A dispersion constraint is identified for $y$-$t$ targets: temporal envelope duration limits transverse spatial resolution through the frequency–wavenumber coupling inherent in dispersive propagation. Carrier-wave modulation circumvents this constraint by shifting the energy into a higher-frequency band. % The experimental robustness is quantified systematically using four target geometries, four propagation distances ($x=3$, 6, 9, and 12~m), and four characteristic steepnesses ($k_0{a}_0=0.072$, 0.145, 0.217, and 0.290), each measured with 21 transverse wave gauges spanning the width of the basin. The prescribed target and experiment are compared in two distinct stages: first, the prescribed target is compared with the constrained solved linear field, and second, the experimentally measured field is compared directly with that solved linear field. The measurements show strong robustness to target shape, propagation distance, and steepness, with the largest departures concentrated at the greatest distance and steepness. Phase-resolved fidelity performance degrades more strongly than the envelope geometry. % In addition, volumetric' inversion of a 3D directional sea state is demonstrated numerically and reduces errors compared to standard boundary matching, achieving a spatio-temporal correlation of 0.90 versus 0.83. These results establish directional wave basins as reconfigurable holographic-style media, enabling the synthesis ofopen-ocean’ environments and designer wave events supporting the de-risking of offshore systems.