tokens: INT-G (intermediate gravity) and FLD-G (field gravity) classes defined by Allers Liu ( 2013 ). In Section 2 , we describe the selected sample of objects presented in this paper. In Section 3 , we provide details of the X-shooter observations and data reduction. In Section 4 , we explain the analysis carried out and our results. In Section 5 , we derive the physical parameters for our sample using evolutionary models for substellar objects. Finally, in Section 6 we summarize our results. 2 SAMPLE SELECTION We selected a sample of 20 benchmark objects with confirmed membership of open clusters or associations, with known ages, metallicities and distances. We chose a sample with photometry and optical spectral types confirming membership. In the case of the Pleiades and Praesepe, members are confirmed not only by photometry and optical spectroscopy, but also by proper motion (Lodieu, Deacon Hambly 2012b ; Boudreault et al. 2012 ; Bouy et al. 2015 ). We selected objects in each of the associations or open clusters with magnitude ranging from J = 14.9 to J = 18.1 mag, which allowed us to obtain spectroscopy with a signal-to-noise ratio of between 4 and 53 in the near-infrared, using exposure times of between 40 min and 1.5 h. Our sample has spectral types between M5.5 and L3.5, with at least one target per open cluster or association of each spectral type between M5.5 and L0. To complete our sample in age range, we added three members from the UppSco association, and four from the Cha I region from proposals: 093.C-0109(A) (P.I. Van der Plas), 093.C-0769(A) (P.I. Bonnefoy) and 095.C-0378(A) (P.I. Testi). We list the objects in our sample with their main characteristics in Table 1 . Table 1. List of observed targets with their full name, coordinates, magnitude, spectral types, cluster or association membership, and flag for disc-bearing sources and binary candidates. Notes . References: [1] Boudreault et al. ( 2010 ), [2] Hodgkin et al. ( 1999 ), [3] Boudreault et al. ( 2012 ), [4] Bouvier et al. ( 1998 ), [5] Stauffer et al. ( 1998 ), [6] Bouvier et al. ( 1998 ), [7] Bouvier et al. ( 1998 ), [8] Nagashima et al. ( 2003 ), [9] Lodieu, Deacon Hambly ( 2012a ), [10] Bihain et al. ( 2006 ), [11] Ardila, Martín Basri ( 2000 ), [12] Martín, Delfosse Guieu ( 2004 ), [13] Lodieu et al. ( 2007 ), [14] Persi et al. ( 2000 ), [15] López Martí et al. ( 2004 ). References of disks detections: [16] Luhman Muench ( 2008 ), [17] van der Plas et al. ( 2016 ), [18] Herczeg et al. ( 2009 ), [19] Long et al. ( 2017 ). a NR: the existence of a disc has not been reported for this object. References for spectral type: [20] Alves de Oliveira et al. ( 2012 ), [21] Luhman ( 2007 ), [22] Luhman ( 2004 ), [23] Lodieu et al. ( 2018 ), [24] Slesnick et al. ( 2008 ), [25] Bihain et al. ( 2010 ), [26] Martín et al. ( 1996 ), [27] Stauffer et al. ( 1998 ), [28] Boudreault Lodieu ( 2013 ), [29] West et al. ( 2011 ), [30] Manara et al. ( 2017 ). References for binary candidates:
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