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Studies on double beta decay processes in <inline-formula><math display="inline"><semantics><msup><mrow></mrow><mn>106</mn></msup></semantics></math></inline-formula>Cd were performed by using a cadmium tungstate scintillator enriched in <inline-formula><math display="inline"><semantics><msup><mrow></mrow><mn>106</mn></msup></semantics></math></inline-formula>Cd at 66% (<inline-formula><math display="inline"><semantics><msup><mrow></mrow><mn>106</mn></msup></semantics></math></inline-formula>CdWO<inline-formula><math display="inline"><semantics><msub><mrow></mrow><mn>4</mn></msub></semantics></math></inline-formula>) with two CdWO<inline-formula><math display="inline"><semantics><msub><mrow></mrow><mn>4</mn></msub></semantics></math></inline-formula> scintillation counters (with natural Cd composition). No effect was observed in the data that accumulated over 26,033 h. New improved half-life limits were set on the different channels and modes of the <inline-formula><math display="inline"><semantics><msup><mrow></mrow><mn>106</mn></msup></semantics></math></inline-formula>Cd double beta decay at level of <inline-formula><math display="inline"><semantics><mrow><mo movablelimits="true" form="prefix">lim</mo><msub><mi>T</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub><mo>∼</mo><msup><mn>10</mn><mn>20</mn></msup><mo>−</mo><msup><mn>10</mn><mn>22</mn></msup></mrow></semantics></math></inline-formula> yr. The limit for the two neutrino electron capture with positron emission in <inline-formula><math display="inline"><semantics><msup><mrow></mrow><mn>106</mn></msup></semantics></math></inline-formula>Cd to the ground state of <inline-formula><math display="inline"><semantics><msup><mrow></mrow><mn>106</mn></msup></semantics></math></inline-formula>Pd, <inline-formula><math display="inline"><semantics><mrow><msubsup><mi>T</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow><mrow><mn>2</mn><mi>ν</mi><mi>EC</mi><msup><mi>β</mi><mo>+</mo></msup></mrow></msubsup><mo>≥</mo><mn>2.1</mn><mo>×</mo><msup><mn>10</mn><mn>21</mn></msup></mrow></semantics></math></inline-formula> yr, was set by the analysis of the <inline-formula><math display="inline"><semantics><msup><mrow></mrow><mn>106</mn></msup></semantics></math></inline-formula>CdWO<inline-formula><math display="inline"><semantics><msub><mrow></mrow><mn>4</mn></msub></semantics></math></inline-formula> data in coincidence with the energy release 511 keV in both CdWO<inline-formula><math display="inline"><semantics><msub><mrow></mrow><mn>4</mn></msub></semantics></math></inline-formula> counters. The sensitivity approaches the theoretical predictions for the decay half-life that are in the range <inline-formula><math display="inline"><semantics><mrow><msub><mi>T</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub><mo>∼</mo><msup><mn>10</mn><mn>21</mn></msup><mo>−</mo><msup><mn>10</mn><mn>22</mn></msup></mrow></semantics></math></inline-formula> yr. The resonant neutrinoless double-electron capture to the 2718 keV excited state of <inline-formula><math display="inline"><semantics><msup><mrow></mrow><mn>106</mn></msup></semantics></math></inline-formula>Pd is restricted at the level of <inline-formula><math display="inline"><semantics><mrow><msubsup><mi>T</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow><mrow><mn>0</mn><mi>ν</mi><mn>2</mn><mi mathvariant="normal">K</mi></mrow></msubsup><mo>≥</mo><mn>2.9</mn><mo>×</mo><msup><mn>10</mn><mn>21</mn></msup></mrow></semantics></math></inline-formula> yr.