Table  of  DSS  for  q=2



In every cell, we give two subsets of {1..n} and corresponding multiset. For instance, in the 1st cell, {3,4,6} and {1,5,7} are two subsets; {* 1^^3, 2^^3, 3^^3, 4^^3, 5^^3, 6^^3 *} is the multiset where 1^^3 means that 1 emerges 3 times. "None" appears if there isn't any pair of subsets at all which introduce the multiset we need.


"P":  the DSS is perfect--each difference appears exactly rho times.
"R":  the DSS is regular--two blocks are of equal size.


        ρ = 1        2
        3
     4    5    6
      n=7 { 1 , 2 }
{ 3, 5 }
{* 1, 2, 3^^2, 4^^2, 5, 6 *}

R
 { 1 , 2 }
{ 3, 5, 7 }
{* 1^^2, 2^^2, 3^^2, 4^^2, 5^^2, 6^^2 *}

P
 { 3, 4, 6 }
{ 1, 5, 7 }
{* 1^^3, 2^^3, 3^^3, 4^^3, 5^^3, 6^^3 *}

P&R
 { 1, 4, 6, 7 }
{ 2, 3, 5 }
{* 1^^4, 2^^4, 3^^4, 4^^4, 5^^4, 6^^4 *}

P
 None
 None
          8 { 1 , 2 }
{ 3, 5 }
{* 1, 2, 3, 4^^2, 5, 6, 7 *}

R
 { 1 , 2 , 3 }
{ 4, 5, 8 }
{* 1^^2, 2^^3, 3^^3, 4^^2, 5^^3, 6^^3,7^^2 *}

R
 { 4, 6, 7, 8 }
{ 2, 3, 5 }
{* 1^^3, 2^^3, 3^^4, 4^^4, 5^^4, 6^^3, 7^^3 *} 		{ 4, 6, 7, 8 }
{ 1, 2, 3, 5 }
{* 1^^4, 2^^4, 3^^6, 4^^4, 5^^6, 6^^4, 7^^4 *}

R
 None None
          9 { 1 , 2 }
{ 3, 5 }
{* 1, 2, 3, 4, 5, 6, 7, 8 *}

P&R
 { 1 , 2 , 3 }
{ 4, 6, 9 }
{* 1^^2, 2^^2, 3^^3, 4^^2, 5^^2, 6^^3, 7^^2, 8^^2 *}

R
 { 4, 5, 6, 9 }
{ 1, 7, 8 }
{* 1^^3, 2^^3, 3^^3, 4^^3, 5^^3, 6^^3, 7^^3, 8^^3 *}

P
 None  None None
          10 { 1 , 2 }
{ 3, 5, 7 }
{* 1, 2, 3, 4^^2, 5^^2, 6^^2, 7, 8, 9 *}
  { 1 , 2 , 3 }
{ 4, 7, 10 }
{* 1^^2, 2^^2, 3^^2, 4^^2, 5^^2, 6^^2, 7^^2, 8^^2, 9^^2 *}

P&R
 { 1, 2, 4, 8 }
{ 5, 7, 9, 10 }
{* 1^^4, 2^^3, 3^^4, 4^^3, 5^^4, 6^^3, 7^^4, 8^^3, 9^^4 *}

R
 { 3, 4, 5, 7, 8 }
{ 1, 2, 6, 9 }
{* 1^^4, 2^^5, 3^^4, 4^^5, 5^^4, 6^^5, 7^^4, 8^^5, 9^^4 *}
  None None
          11 { 1 , 2 }
{ 3, 5, 7 }
{* 1, 2, 3, 4, 5^^2, 6^^2, 7, 8, 9, 10 *}
 { 1 , 2 , 3 }
{ 4, 5, 8, 11 }
{* 1^^2, 2^^3, 3^^3, 4^^2, 5^^2, 6^^2, 7^^2, 8^^3, 9^^3, 10^^2 *}
 { 1, 8, 9, 10 }
{ 3, 5, 7, 11 }
{* 1^^3, 2^^3, 3^^3, 4^^3, 5^^4, 6^^4, 7^^3, 8^^3, 9^^3, 10^^3 *}

R
 None
 { 3, 4, 5, 7, 10 }
{ 1, 2, 6, 9, 11 }
{* 1^^5, 2^^5, 3^^5, 4^^5, 5^^5, 6^^5, 7^^5, 8^^5, 9^^5, 10^^5 *}

P&R
 { 1, 2, 4, 5, 6, 10 }
{ 3, 7, 8, 9, 11 }
{* 1^^6, 2^^6, 3^^6, 4^^6, 5^^6, 6^^6, 7^^6, 8^^6, 9^^6, 10^^6 *}

P
          12 { 1 , 2 }
{ 3, 5, 7 }
{* 11, 1, 2, 3, 4, 5, 6^^2, 7, 8, 9, 10 *}
 { 1 , 2 , 3 }
{ 4, 6, 9, 12 }
{* 11^^2, 1^^2, 2^^2, 3^^3, 4^^2, 5^^2, 6^^2, 7^^2, 8^^2, 9^^3, 10^^2 *}
 { 3, 5, 6, 7, 11 }
{ 1, 2, 4, 9 }
{* 11^^3, 1^^3, 2^^5, 3^^4, 4^^3, 5^^3, 6^^4, 7^^3, 8^^3, 9^^4, 10^^5 *} 		{ 3, 5, 6, 7, 11 }
{ 1, 2, 4, 9, 10 }
{* 11^^4, 1^^4, 2^^5, 3^^5, 4^^4, 5^^5, 6^^4, 7^^5, 8^^4, 9^^5, 10^^5 *}

R 		 { 1, 3, 4, 6, 8, 12 }
{ 2, 7, 9, 10, 11 }
{*  1^^6, 2^^5, 3^^5, 4^^5, 5^^5, 6^^8, 7^^5, 8^^5, 9^^5, 10^^5,11^^6 *} 		{ 1, 3, 4, 6, 8, 12 }
{ 2, 5, 7, 9, 10, 11 }
{* 1^^8, 2^^6, 3^^6, 4^^6, 5^^6, 6^^8, 7^^6, 8^^6, 9^^6, 10^^6,11^^8 *}

R
          13 { 1 , 2 }
{ 3, 5, 7 }
{* 11, 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 *}

P
 { 1 , 2 , 3 }
{ 4, 7, 10, 13 }
{* 11^^2, 1^^2, 12^^2, 2^^2, 3^^2, 4^^2, 5^^2, 6^^2, 7^^2, 8^^2, 9^^2, 10^^2 *}

P
 { 1, 8, 9, 12, 13 }
{ 2, 4, 7, 10 }
{* 11^^4, 12^^3, 1^^3, 2^^4, 3^^3, 4^^3, 5^^3, 6^^4, 7^^4, 8^^3, 9^^3, 10^^3 *} 		{ 2, 4, 5, 7, 10, 11 }
{ 1, 3, 12, 13 }
{* 11^^4, 1^^4, 12^^4, 2^^4, 3^^4, 4^^4, 5^^4, 6^^4, 7^^4, 8^^4, 9^^4, 10^^4 *}

P
 { 2, 3, 5, 10, 11, 12 }
{ 4, 6, 7, 9, 13 }
{*  1^^5, 2^^5, 3^^5, 4^^5, 5^^5, 6^^5, 7^^5, 8^^5, 9^^5, 10^^5,11^^5, 12^^5 *}

P 		 { 5, 6, 8, 10, 12, 13 }
{ 1, 2, 3, 4, 7, 11 }
{* 1^^6, 2^^6, 3^^6, 4^^6, 5^^6, 6^^6, 7^^6, 8^^6, 9^^6, 10^^6, 11^^6, 12^^6 *}

P&R
          14 { 1 , 2 , 3 }
{ 4, 7, 10 }
{* 11, 12, 1, 13, 2, 3, 4, 5^^2, 6^^2, 7^^2, 8^^2, 9^^2, 10 *}

R
 { 1 , 2 , 3 , 4 }
{ 5, 6, 10, 14 }
{* 11^^3, 1^^2, 12^^3, 2^^3, 13^^2, 3^^3, 4^^3, 5^^2, 6^^2, 7^^2, 8^^2, 9^^2,
10^^3 *}

R
 { 1, 6, 9, 11, 12 }
{ 2, 3, 8, 14 }
{* 1^^3, 2^^3, 3^^3, 4^^3, 5^^3, 6^^3, 7^^4, 8^^3, 9^^3, 10^^3, 11^^3, 12^^3, 13^^3 *} 		{ 1, 3, 6, 9, 13, 14 }
{ 4, 5, 7, 10, 12 }
{* 11^^4, 1^^5, 12^^4, 2^^4, 13^^5, 3^^4, 4^^6, 5^^5, 6^^4, 7^^4, 8^^4, 9^^5, 10^^6 *}
 { 1, 3, 6, 9, 13, 14 }
{ 4, 7, 8, 10, 11, 12 }
{*  1^^5, 2^^6,  3^^5, 4^^5, 5^^7, 6^^5, 7^^6, 8^^5, 9^^7, 10^^5 ,11^^5, 12^^6,13^^5*}

R
 { 6, 7, 8, 9, 11, 13, 14 }
{ 1, 2, 4, 5, 10, 12 }
{* 1^^6, 2^^6, 3^^6, 4^^8, 5^^7, 6^^6, 7^^6, 8^^6, 9^^7,
10^^8, 11^^6, 12^^6, 13^^6 *} 
          15 { 1 , 2 , 3 }
{ 4, 7, 10 }
{* 1, 2, 3, 4, 5, 6^^2, 7^^2, 8^^2, 9^^2, 10, 11, 12, 13, 14 *}

R
 { 1 , 2 , 3 , 4 }
{ 5, 7, 11, 15 }
{* 1^^2, 2^^2, 3^^3, 4^^3, 5^^2, 6^^2, 7^^2, 8^^2, 9^^2, 10^^2,11^^3, 12^^3,
13^^2, 14^^2 *}

R
 { 1, 4, 6, 14, 15 }
{ 2, 5, 9, 12, 13 }
{* 1^^4, 2^^4, 3^^4, 4^^3, 5^^3, 6^^4, 7^^3, 8^^3, 9^^4, 10^^3, 11^^3, 12^^4, 13^^4, 14^^4 *}

R
 { 1, 3, 6, 9, 13, 14 }
{ 2, 8, 10, 11, 12 }
{* 1^^5, 2^^4, 3^^4, 4^^5, 5^^4, 6^^4, 7^^4, 8^^4, 9^^4, 10^^4, 11^^5, 12^^4, 13^^4, 14^^5 *}
 { 4, 5, 8, 10, 12, 14 }
{ 1, 2, 3, 6, 13, 15 }
{* 1^^5, 2^^5, 3^^5, 4^^5, 5^^5, 6^^5, 7^^6, 8^^6, 9^^5, 10^^5, 11^^5, 12^^5, 13^^5, 14^^5 *}

R 		   None
          16 { 1 , 2 , 3 }
{ 4, 7, 10 }
{* 1, 2, 3, 4, 5, 6, 7^^2, 8^^2, 9^^2, 10, 11, 12, 13, 14, 15 *}

R
 { 1 , 2 , 3 , 4 }
{ 5, 8, 12, 16 }
{* 1^^2, 2^^2, 3^^2, 4^^3, 5^^2, 6^^2, 7^^2, 8^^2, 9^^2, 10^^2, 11^^2, 12^^3,
13^^2, 14^^2, 15^^2 *}

R
 { 1, 4, 6, 14, 15 }
{ 2, 5, 8, 9, 12 }
{* 1^^3, 2^^3, 3^^3, 4^^4, 5^^3, 6^^4, 7^^3, 8^^4, 9^^3, 10^^4, 11^^3, 12^^4, 13^^3, 14^^3, 15^^3 *}

R
 { 2, 3, 6, 7, 9, 15 }
{ 5, 8, 10, 11, 12 }
{* 1^^4, 2^^4, 3^^4, 4^^4, 5^^4, 6^^4, 7^^4, 8^^4, 9^^4, 10^^4, 11^^4, 12^^4, 13^^4, 14^^4, 15^^4 *}

P
 { 1, 2, 5, 8, 10, 14, 15 }
{ 4, 6, 7, 9, 11, 12 }
{* 1^^6, 2^^5, 3^^5, 4^^6, 5^^5, 6^^7, 7^^5, 8^^6, 9^^5, 10^^7, 11^^5, 12^^6, 13^^5, 14^^5, 15^^6 *}
 { 1, 6, 7, 10, 12, 14, 15 }
{ 2, 3, 4, 5, 8, 9, 11 }
{* 1^^6, 2^^6, 3^^7, 4^^8, 5^^6, 6^^7, 7^^6, 8^^6, 9^^6, 10^^7, 11^^6, 12^^8, 13^^7, 14^^6, 15^^6 *}

R
          17
 { 1 , 2 , 3 }
{ 4, 7, 10 }
{* 1, 2, 3, 4, 5, 6, 7, 8^^2, 9^^2, 10, 11, 12, 13, 14, 15, 16 *}

R
 { 1 , 2 , 3 , 4 }
{ 5, 9, 13, 17 }
{* 1^^2, 2^^2, 3^^2, 4^^2, 5^^2, 6^^2, 7^^2, 8^^2, 9^^2, 10^^2, 11^^2, 12^^2,
13^^2, 14^^2, 15^^2, 16^^2 *}

P&R
 { 1, 4, 6, 14, 15 }
{ 2, 7, 11, 12, 13 }
{* 1^^3, 2^^3, 3^^3, 4^^3, 5^^3, 6^^3, 7^^4, 8^^3, 9^^3, 10^^4, 11^^3, 12^^3, 13^^3, 14^^3, 15^^3, 16^^3 *}

R
 { 1, 3, 6, 12, 13, 17 }
{ 5, 7, 10, 11, 14, 15 }
{* 1^^4, 2^^6, 3^^4, 4^^4, 5^^4, 6^^4, 7^^5, 8^^5, 9^^5, 10^^5, 11^^4, 12^^4, 13^^4, 14^^4, 15^^6, 16^^4 *}

R
 { 3, 4, 12, 13, 14, 15, 17 }
{ 1, 2, 5, 6, 7, 16 }
{* 1^^5, 2^^6, 3^^5, 4^^5, 5^^5, 6^^5, 7^^6, 8^^5, 9^^5, 10^^6, 11^^5, 12^^5, 13^^5, 14^^5, 15^^6, 16^^5 *}
 { 3, 5, 9, 13, 14, 15, 17 }
{ 1, 2, 4, 7, 8, 11, 12 }
{* 1^^6, 2^^7, 3^^6, 4^^6, 5^^6, 6^^6, 7^^6, 8^^6, 9^^6, 10^^6, 11^^6, 12^^6, 13^^6, 14^^6, 15^^7, 16^^6 *}

R
          18
 { 1 , 2 , 3 }
{ 4, 7, 10 }
{* 17, 1, 2, 3, 4, 5, 6, 7, 8, 9^^2, 10, 11, 12, 13, 14, 15, 16 *}

R
 { 1 , 2 , 3 , 4 }
{ 5, 6, 10, 14, 18 }
{* 17^^2, 1^^2, 2^^3, 3^^3, 4^^3, 5^^2, 6^^2, 7^^2, 8^^2, 9^^2, 10^^2, 11^^2, 12^^2, 13^^2, 14^^3, 15^^3, 16^^3 *}


 { 1, 3, 6, 12, 13, 17 }
{ 5, 8, 9, 10, 18 }
{* 17^^3, 1^^3, 2^^3, 3^^4, 4^^4, 5^^3, 6^^4, 7^^4, 8^^3, 9^^4, 10^^3, 11^^4, 12^^4, 13^^3, 14^^4, 15^^4, 16^^3 *}
 { 1, 3, 6, 12, 13, 17 }
{ 5, 8, 9, 10, 11, 18 }
{* 1^^4, 2^^4, 3^^4, 4^^4, 5^^4, 6^^5, 7^^4, 8^^5, 9^^4, 10^^5, 11^^4, 12^^5, 13^^4, 14^^4, 15^^4, 16^^4 ,17^^4, *}

R
 { 1, 4, 11, 13, 14, 16, 18 }
{ 2, 3, 8, 9, 10, 15, 17 }
{*  1^^7, 2^^6, 3^^5, 4^^7, 5^^5, 6^^5, 7^^5, 8^^6, 9^^6, 10^^6, 11^^5, 12^^5, 13^^5, 14^^7, 15^^5, 16^^6, 17^^7,*}

R
 { 1, 3, 11, 12, 15, 16, 17, 18 }
{ 2, 4, 6, 7, 10, 13, 14 }
{* 1^^6, 2^^6, 3^^6, 4^^6, 5^^8, 6^^6, 7^^7, 8^^7, 9^^8, 10^^7, 11^^7, 12^^6, 13^^8, 14^^6, 15^^6, 16^^6,  17^^6 *}
          19
 { 1 , 2 , 3 }
{ 4, 7, 10 }
{* 17, 1, 18, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 *}

P&R
 { 1 , 2 , 3 , 4 }
{ 5, 7, 11, 15, 19 }
{* 17^^2, 1^^2, 18^^2, 2^^2, 3^^3, 4^^3, 5^^2, 6^^2, 7^^2, 8^^2, 9^^2, 10^^2, 11^^2, 12^^2, 13^^2, 14^^2, 15^^3,
16^^3 *}
 { 1, 3, 6, 12, 13, 17 }
{ 4, 5, 7, 8, 9 }
{* 17^^3, 1^^3, 18^^3, 2^^3, 3^^3, 4^^4, 5^^3, 6^^4, 7^^3, 8^^4, 9^^3, 10^^3, 11^^4, 12^^3, 13^^4, 14^^3, 15^^4, 16^^3 *}
 { 3, 11, 14, 17, 18, 19 }
{ 6, 8, 10, 13, 15, 16 }
{* 1^^4,  2^^4, 3^^4, 4^^4, 5^^4, 6^^4, 7^^4, 8^^4, 9^^4, 10^^4,
11^^4, 12^^4, 13^^4, 14^^4, 15^^4, 16^^4,17^^4, 18^^4*}

P&R
 { 1, 4, 11, 13, 14, 16, 18 }
{ 2, 3, 6, 7, 9, 15, 17 }
{*  1^^6,  2^^5, 3^^5, 4^^5, 5^^6, 6^^5, 7^^5, 8^^7, 9^^5, 10^^5, 11^^7, 12^^5, 13^^5, 14^^6, 15^^5, 16^^5, 17^^5,  18^^6*}

R
 { 4, 6, 8, 9, 11, 12, 18, 19 }
{ 1, 2, 5, 7, 13, 15, 17 }
{* 1^^7, 2^^6, 3^^6, 4^^6, 5^^6, 6^^7, 7^^6, 8^^6, 9^^6, 10^^6, 11^^6, 12^^6, 13^^7, 14^^6, 15^^6, 16^^6,  17^^6, 18^^7 *}
          20
 { 1 , 2 , 3 }
{ 4, 7, 10, 13}
{* 17, 1, 18, 19, 2, 3, 4, 5, 6, 7, 8^^2,9^^2, 10^^2, 11^^2, 12^^2, 13, 14, 15,
16 *}
 { 1 , 2 , 3 , 4 }
{ 5, 8, 12, 16, 20 }
{* 17^^2, 1^^2, 18^^2, 2^^2, 19^^2, 3^^2, 4^^3, 5^^2, 6^^2, 7^^2, 8^^2, 9^^2,
10^^2, 11^^2, 12^^2, 13^^2, 14^^2, 15^^2, 16^^3 *}
 { 6, 11, 13, 15, 16, 18 }
{ 1, 5, 9, 14, 20 }
{* 17^^3, 1^^3, 18^^3, 2^^3, 19^^3, 3^^3, 4^^3, 5^^3, 6^^4, 7^^3, 8^^3, 9^^3, 10^^4, 11^^3, 12^^3, 13^^3, 14^^4, 15^^3,
16^^3 *}
 { 1, 4, 11, 13, 14, 16, 18 }
{ 3, 7, 8, 9, 15, 19 }
{*  1^^4, 2^^4,  3^^4, 4^^4, 5^^6, 6^^5, 7^^4, 8^^4, 9^^5, 10^^4, 11^^5, 12^^4, 13^^4, 14^^5, 15^^6, 16^^4 ,17^^4,18^^4, 19^^4*}
 { 2, 4, 5, 9, 10, 13, 15 }
{ 3, 6, 7, 14, 16, 18, 20 }
{* 1^^6,  2^^5,  3^^5, 4^^5, 5^^5, 6^^5, 7^^5, 8^^5, 9^^5, 10^^6, 11^^5, 12^^5, 13^^5, 14^^5,15^^5,16^^5, 17^^5, 18^^5, 19^^6 *}

R
 { 4, 6, 8, 9, 11, 12, 18, 19 }
{ 1, 3, 5, 10, 14, 15, 16, 17 }
{* 1^^6, 2^^6, 3^^8, 4^^7, 5^^7, 6^^7, 7^^6, 8^^7, 9^^7, 10^^6, 11^^7, 12^^7, 13^^6, 14^^7, 15^^7, 16^^7,  17^^8, 18^^6, 19^^6 *}

R
          21
 { 1 , 2 , 3 }
{ 4, 7, 10, 13}
{* 17, 1, 18, 19, 2, 20, 3, 4, 5, 6, 7, 8, 9^^2, 10^^2, 11^^2, 12^^2, 13, 14,
15, 16 *}
 { 1 , 2 , 3 , 4 }
{ 5, 9, 13, 17, 21 }
{* 17^^2, 1^^2, 18^^2, 2^^2, 19^^2, 3^^2, 20^^2, 4^^2, 5^^2, 6^^2, 7^^2, 8^^2,
9^^2, 10^^2, 11^^2, 12^^2, 13^^2, 14^^2, 15^^2, 16^^2 *}

P
 { 2, 4, 5, 6, 8, 10 }
{ 1, 7, 12, 17, 21 }
{* 17^^3, 1^^3, 18^^3, 2^^3, 19^^3, 3^^3, 20^^3, 4^^3, 5^^3, 6^^3, 7^^3, 8^^3, 9^^3, 10^^3, 11^^3, 12^^3, 13^^3, 14^^3, 15^^3, 16^^3 *}

P
 { 1, 4, 11, 13, 14, 16, 18 }
{ 2, 5, 8, 15, 19, 20 }
{*  1^^5,  2^^4, 19^^4, 3^^4,  4^^4, 5^^4, 6^^5, 7^^4, 8^^4, 9^^4, 10^^4, 11^^4, 12^^4, 13^^4, 14^^4, 15^^5, 16^^4,17^^4,18^^4, 20^^5*}
 { 4, 6, 8, 10, 11, 12, 17, 19 }
{ 2, 3, 9, 13, 14, 15, 18 }
{*  1^^6, 2^^5, 3^^7,  4^^6, 5^^6, 6^^5, 7^^6, 8^^5, 9^^5, 10^^5, 11^^5, 12^^5, 13^^5, 14^^6, 15^^5, 16^^6, 17^^6, 18^^7, 19^^5, 20^^6, *}
 { 4, 6, 8, 10, 11, 12, 17, 19 }
{ 2, 3, 9, 13, 14, 15, 18, 21 }
{* 1^^6, 2^^6, 3^^7, 4^^8, 5^^6, 6^^6, 7^^6, 8^^6, 9^^6, 10^^7, 11^^7, 12^^6, 13^^6, 14^^6, 15^^6, 16^^6,  17^^8,  18^^7,  19^^6,  20^^6 *}

R
          22
 { 1 , 2 , 3 }
{ 4, 7, 10, 13 }
{* 1, 2, 3, 4, 5, 6, 7, 8, 9, 10^^2, 11^^2, 12^^2, 13, 14, 15, 16, 17, 18, 19, 20, 21 *}
 { 1 , 2 , 3 , 4 , 5 }
{ 6, 7, 12, 17, 22 }
{* 1^^2, 2^^3, 3^^3, 4^^3, 5^^3, 6^^2, 7^^2, 8^^2, 9^^2, 10^^2, 11^^2, 12^^2,
13^^2, 14^^2, 15^^2, 16^^2, 17^^3, 18^^3, 19^^3, 20^^3, 21^^2 *}

R
 { 6, 11, 13, 15, 16, 18 }
{ 4, 5, 10, 14, 20, 21 }
{* 1^^4, 2^^3, 3^^3, 4^^3, 5^^3, 6^^3, 7^^3, 8^^6, 9^^3, 10^^3, 11^^4, 12^^3, 13^^3, 14^^6, 15^^3, 16^^3, 17^^3, 18^^3, 19^^3, 20^^3, 21^^4 *}

R
 { 6, 11, 12, 13, 14, 21, 22 }
{ 1, 3, 7, 15, 16, 20 }
{* 1^^4, 2^^4, 3^^4, 4^^4, 5^^4, 6^^4, 7^^4, 8^^4, 9^^4, 10^^4, 11^^4, 12^^4, 13^^4, 14^^4, 15^^4, 16^^4, 17^^4, 18^^4, 19^^4, 20^^4, 21^^4 *}

P
 { 1, 3, 9, 10, 11, 12, 15, 16 }
{ 2, 4, 5, 7, 14, 18, 22 }
{* 1^^5, 2^^5, 3^^5, 4^^5, 5^^5, 6^^5, 7^^6, 8^^5, 9^^6, 10^^5, 11^^8, 12^^5, 13^^6, 14^^5, 15^^6, 16^^5, 17^^5, 18^^5, 19^^5, 20^^5, 21^^5 *}
 { 2, 3, 5, 7, 13, 14, 20, 21 }
{ 4, 6, 9, 10, 11, 12, 18, 19 }
{* 1^^6, 2^^6, 3^^6, 4^^6, 5^^7, 6^^6, 7^^6, 8^^6, 9^^6, 10^^6, 11^^6, 12^^6, 13^^6, 14^^6, 15^^6, 16^^6, 17^^7, 18^^6, 19^^6, 20^^6, 21^^6 *}

R
          23
 { 1 , 2 , 3 }
{ 4, 7, 10, 13 }
{* 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11^^2, 12^^2, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22 *}
 { 1 , 2 , 3 , 4 , 5 }
{ 6, 8, 13, 18, 23 }
{* 1^^2, 2^^2, 3^^3, 4^^3, 5^^3, 6^^2, 7^^2, 8^^2, 9^^2, 10^^2, 11^^2, 12^^2,
13^^2, 14^^2, 15^^2, 16^^2, 17^^2, 18^^3, 19^^3, 20^^3, 21^^2, 22^^2 *}

R
 { 1, 3, 6, 12, 13, 17 }
{ 2, 8, 14, 20, 22, 23 }
{* 1^^4, 2^^3, 3^^3, 4^^4, 5^^3, 6^^3, 7^^3, 8^^3, 9^^3, 10^^4, 11^^3, 12^^3, 13^^4, 14^^3, 15^^3, 16^^3, 17^^3, 18^^3, 19^^4, 20^^3, 21^^3, 22^^4 *}

R
 { 1, 2, 4, 16, 19, 21, 23 }
{ 5, 8, 12, 14, 17, 18, 22 }
{* 1^^5, 2^^4, 3^^4, 4^^4, 5^^4, 6^^4, 7^^6, 8^^4, 9^^4, 10^^5, 11^^5, 12^^5, 13^^5, 14^^4, 15^^4, 16^^6, 17^^4, 18^^4, 19^^4, 20^^4, 21^^4, 22^^5 *}

R
 { 1, 3, 4, 7, 9, 11, 15, 16 }
{ 5, 8, 12, 17, 18, 21, 22 }
{* 1^^5, 2^^5, 3^^5, 4^^5, 5^^5, 6^^6, 7^^5, 8^^5, 9^^5, 10^^5, 11^^5, 12^^5,
13^^5, 14^^5, 15^^5, 16^^5, 17^^6, 18^^5, 19^^5, 20^^5, 21^^5, 22^^5 *}
 { 4, 5, 11, 14, 15, 17, 19, 21, 23 }
{ 1, 2, 8, 9, 10, 12, 13, 22 }
{*  1^^6, 2^^6, 3^^7, 4^^6, 5^^8, 6^^6, 7^^6, 8^^7, 9^^7, 10^^7, 11^^6, 12^^6, 13^^7, 14^^7, 15^^7, 16^^6, 17^^6, 18^^8, 19^^6,  20^^7,  21^^6,  22^^6, *}
          24
 { 1 , 2 , 3 }
{ 4, 7, 10, 13 }
{* 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12^^2, 13, 14, 15, 16, 17, 18, 19, 20, 21,22, 23 *}
 { 1 , 2 , 3 , 4 , 5 }
{ 6, 9, 14, 19, 24 }
{* 1^^2, 2^^2, 3^^2, 4^^3, 5^^3, 6^^2, 7^^2, 8^^2, 9^^2, 10^^2, 11^^2, 12^^2,
13^^2, 14^^2, 15^^2, 16^^2, 17^^2, 18^^2, 19^^3, 20^^3, 21^^2, 22^^2, 23^^2 *}

R
 { 2, 3, 5, 12, 14, 18 }
{ 6, 16, 17, 19, 20, 23 }
{* 1^^3, 2^^3, 3^^3, 4^^3, 5^^3, 6^^4, 7^^3, 8^^3, 9^^3, 10^^3, 11^^3, 12^^4, 13^^3, 14^^3, 15^^3, 16^^3, 17^^3, 18^^4,19^^3, 20^^3, 21^^3, 22^^3,23^^3 *}

R
 { 1, 2, 4, 16, 19, 21, 23 }
{ 6, 7, 8, 14, 18, 22, 24 }
{*  1^^5,  2^^4, 3^^5, 4^^4, 5^^5,
6^^4, 7^^4, 8^^4, 9^^4, 10^^4, 11^^4, 12^^4, 13^^4, 14^^4, 15^^4, 16^^4 ,17^^4,18^^4,19^^5, 20^^4, 21^^5, 22^^4, 23^^5, *}

R
 { 3, 5, 8, 12, 18, 19, 23, 24 }
{ 4, 6, 10, 11, 13, 14, 15, 16 }
{* 1^^5, 2^^5, 3^^5, 4^^5, 5^^5, 6^^5, 7^^5, 8^^8, 9^^5, 10^^6, 11^^7, 12^^6, 13^^7, 14^^6, 15^^5, 16^^8, 17^^5, 18^^5, 19^^5, 20^^5, 21^^5, 22^^5, 23^^5 *}

R
 ???
          25
 { 1 , 2 , 3 }
{ 4, 7, 10, 13 }
{* 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21,
22, 23, 24 *}

P
 { 1 , 2 , 3 , 4 , 5 }
{ 6, 10, 15, 20, 25 }
{* 1^^2, 2^^2, 3^^2, 4^^2, 5^^3, 6^^2, 7^^2, 8^^2, 9^^2, 10^^2, 11^^2, 12^^2,
13^^2, 14^^2, 15^^2, 16^^2, 17^^2, 18^^2, 19^^2, 20^^3, 21^^2, 22^^2, 23^^2, 24^^2 *}

R
 { 1, 8, 14, 17, 20, 21 }
{ 2, 3, 5, 13, 22, 23 }
{* 1^^3, 2^^3, 3^^3, 4^^3, 5^^3, 6^^3, 7^^3, 8^^3, 9^^3, 10^^3, 11^^3, 12^^3, 13^^3, 14^^3, 15^^3, 16^^3, 17^^3, 18^^3, 19^^3, 20^^3, 21^^3, 22^^3, 23^^3, 24^^3 *}

P&R
 { 1, 2, 4, 16, 19, 21, 23 }
{ 8, 12, 13, 14, 22, 24, 25 }
{* 1^^4, 2^^4, 3^^4, 4^^5, 5^^4, 6^^4, 7^^4, 8^^4, 9^^4, 10^^4, 11^^4, 12^^4, 13^^4, 14^^4, 15^^4, 16^^4, 17^^4, 18^^4, 19^^4, 20^^4, 21^^5, 22^^4, 23^^4, 24^^4 *}

R
 { 1, 2, 3, 8, 13, 14, 20, 23 }
{ 7, 9, 11, 15, 17, 18, 21, 24 }
{* 1^^5, 2^^5, 3^^5, 4^^6, 5^^6, 6^^5, 7^^5, 8^^5, 9^^7, 10^^5, 11^^5, 12^^5, 13^^5, 14^^5, 15^^5, 16^^7, 17^^5, 18^^5, 19^^5, 20^^6, 21^^6, 22^^5, 23^^5, 24^^5 *}

R
 ???