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The Maunakea Spectroscopic Explorer (MSE) is a next-generation observatory, designed to provide highly multiplexed, multi-object spectroscopy over a wide field of view. The observatory will consist of (1) a telescope with an 11.25 m aperture, (2) a 1.5 square-degree science field of view, (3) fibre optic positioning and transmission systems, and (4) a suite of low (R=3000), moderate (R=6000) and high resolution (R=40,000) spectrographs. The Fibre Transmission System (FiTS) consists of 4332 optical fibres, designed to transmit the light from the telescope prime focus to the dedicated spectrographs. The ambitious science goals of MSE require the Fibre Transmission System to deliver performance well beyond the current state of the art for multi-fibre systems, e.g., the sensitivity to observe magnitude 24 objects (@ SNR=2) over a very broad wavelength range (0.37 – 1.8 μm) while achieving relative spectrophotometric accuracy of < 3% and radial velocity precision of 20 km/s (@ SNR=5). This paper details the design of the FiTS fibre system. It places FiTS into context with existing and planned spectroscopic facilities, such as Subaru/PFS, KPNO/DESI, ESO/4MOST and Gemini/GRACES. The results and lessons learned from GRACES are particularly applicable, since FiTS and GRACES share many team members, including industrial partner FiberTech Optica (Kitchener, ON). The FiTS system consists of 57 identical fibre cables. These cables have been designed to be modular, facilitating efficient construction and automated acceptance testing. Each cable consists of 76 fibres, including 57 fibres feeding light to the low and moderate resolution spectrographs and 19 fibres feeding the high-resolution spectrographs. Thus, the MSE/FiTS consists of 4332 fibres in total. Novel construction techniques utilizing continuous high-NA (f/2) fibres, pioneered by FiberTech Optica, are outlined and test results showing < 5% focal ratio degradation (FRD) in V-band are presented. The effect on FRD from varying the input f/# is also shown. Where test data is unavailable, system error budgets have been created to assess design choices on options such as fibre material, anti-reflection coatings, and fibre-optic connectors
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