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This work is devoted to the study of the possibility of obtaining the highest O2(a 1Dg) yield in ED SOG at the high absolute O2(a 1Dg) concentration needed for developing a powerful oxygen-iodine laser pumped by electric discharge. A singlet oxygen was produced in a transversal rf discharge in the pressure range 10-30 Torr of pure oxygen in the small-diameter (7 mm) quartz tube with HgO coating of the inner walls for removing atomic oxygen to eliminate fast O2(a 1Dg) quenching. It is shown that pd scaling (p--pressure, d--tube diameter) of the rf discharge actually allows an increase of the absolute O2(a 1Dg) density. The increase in the rf frequency from 13.56 to 81 MHz results in the essential increase of the O2(a 1Dg) yield (beyond 15% at such a high oxygen pressure as 15 Torr), but the subsequent transfer to the higher rf frequency of 160 MHz only slightly influences the maximally obtained O2(a 1Dg) yield. The effect of the NO admixture on the O2(a 1Dg) production has been also studied. The rate constant of O2(a 1Dg) quenching by {\rm NO}k_{q}^{\rm NO}=(8.5\pm 1.5)\times 10^{-17}\,{\rm cm}^{3}\, {\rm s}^{-1} was directly measured. The NO admixture (up to 20%) resulted in the noticeable increase in the O2(a 1Dg) yield mainly at low energy inputs. But this gain in the O2(a 1Dg) concentration drops with increasing energy input. Nevertheless it is shown that by combining the O2 + NO mixture with the HgO coating of the discharge tube walls one can provide the O2(a 1Dg) yield on the level of [?]21% at 10 Torr, [?]17% at 20 Torr and [?]13% at 30 Torr of O2 with the efficiency of [?]4-6%. The analysis of the NO admixture influence on the discharge structure and O2(a 1Dg) production has been carried out by using the 2D model. It was found that at the low energy input the NO admixture acts as an easily ionized species that enlarges the region occupied by plasma. Thus, in the O2 + NO discharge the normal current density is lower than in the pure oxygen discharge. As a result a higher energetic efficiency of O2(a 1Dg) production is also observed in the case of the O2 + NO mixture and the low energy input. In order to provide the optimal conditions for O2(a 1Dg) production (with regard to the yield and efficiency) in the continuous wave transversal VHF discharge at such high oxygen pressures as of 10-30 Torr it is necessary to find out the range of energy inputs where the VHF discharge operates in the regime of normal current density on the boundary with the abnormal regime and to remove atomic oxygen produced in the discharge by some volume or surface processes. [ABSTRACT FROM AUTHOR]