# Multisets with 4 Elements

## n=5, k=4, 70 multisets

Rectangle 14x5
 2-2-2-2 2-2-2-4 2-2-4-4 2-4-4-4 4-4-4-4 4-4-4-5 4-4-5-5 4-5-5-5 5-5-5-5 3-5-5-5 1-3-5-5 1-1-5-5 1-1-1-5 1-1-2-5 1-2-2-2 1-2-2-4 1-2-4-4 1-4-4-4 3-4-4-4 3-4-4-5 3-4-5-5 2-4-5-5 2-5-5-5 1-5-5-5 1-4-5-5 1-1-4-5 1-1-3-5 1-1-2-3 1-1-2-2 1-1-2-4 1-1-4-4 1-3-4-4 3-3-4-4 3-3-4-5 3-3-5-5 2-3-5-5 2-2-5-5 1-2-5-5 1-2-4-5 1-4-4-5 1-3-4-5 1-2-3-5 1-1-1-2 1-1-1-4 1-1-3-4 1-3-3-4 3-3-3-4 3-3-3-5 2-3-3-5 2-2-3-5 2-2-2-5 1-2-2-5 2-2-4-5 2-4-4-5 2-3-4-5 1-2-3-4 1-1-1-1 1-1-1-3 1-1-3-3 1-3-3-5 1-3-3-3 3-3-3-3 2-3-3-3 2-2-3-3 2-2-2-3 1-2-2-3 2-2-3-4 2-3-4-4 2-3-3-4 1-2-3-3

The Rectangle of size 10x7 with real pieces.

You can also get a spiral, and it's easy because the number of touching sides is much lower.

## n=6, k=4, 126 multisets

Rectangle 42x3

With multisets from 1..6
 2-3-3-3 3-3-3-5 3-3-4-5 3-4-4-5 4-4-4-5 4-4-5-6 4-4-6-6 2-4-6-6 2-2-6-6 1-2-2-6 1-1-2-2 1-2-2-4 2-2-4-5 2-4-5-6 4-5-6-6 4-6-6-6 3-4-6-6 3-3-6-6 2-3-6-6 1-2-3-6 1-1-2-3 1-1-2-4 1-1-4-4 1-1-4-6 1-4-6-6 1-2-4-6 1-2-3-4 1-2-4-5 1-1-4-5 1-1-5-5 1-5-5-6 1-2-5-5 2-4-5-5 4-5-5-6 3-4-5-6 2-3-4-6 2-2-3-4 2-2-3-6 2-3-5-6 3-5-6-6 1-5-6-6 1-4-5-6 3-3-3-6 1-3-3-3 1-3-3-4 1-3-4-4 1-4-4-4 4-4-4-6 2-4-4-6 2-2-4-6 2-2-2-6 1-2-2-2 1-2-2-3 1-2-2-5 2-2-2-5 2-2-5-6 2-5-6-6 2-6-6-6 3-6-6-6 1-3-6-6 1-2-6-6 1-1-2-6 1-1-1-2 1-1-1-4 1-1-3-4 1-1-3-6 1-3-4-6 1-4-4-6 1-2-4-4 1-4-4-5 1-4-5-5 1-5-5-5 5-5-5-6 2-5-5-5 2-3-5-5 3-5-5-6 3-4-5-5 2-3-4-5 2-3-3-4 2-3-3-6 3-3-5-6 1-3-5-6 1-1-5-6 1-2-5-6 3-3-3-3 3-3-3-4 3-3-4-4 3-4-4-4 4-4-4-4 2-4-4-4 2-2-4-4 2-2-2-4 2-2-2-2 2-2-2-3 2-2-3-3 2-2-3-5 2-2-5-5 2-5-5-6 5-5-6-6 5-6-6-6 6-6-6-6 1-6-6-6 1-1-6-6 1-1-1-6 1-1-1-1 1-1-1-3 1-1-3-3 1-3-3-6 3-3-4-6 3-4-4-6 2-3-4-4 2-4-4-5 4-4-5-5 4-5-5-5 5-5-5-5 3-5-5-5 3-3-5-5 1-3-5-5 1-3-4-5 1-2-3-5 2-3-3-5 1-2-3-3 1-3-3-5 1-1-3-5 1-1-1-5 1-1-2-5

Rectangle 21x6

With multisets from 1..6
 6-6-6-6 5-6-6-6 5-5-6-6 5-5-5-6 5-5-5-5 3-5-5-5 3-4-5-5 3-4-4-5 3-4-4-4 2-3-4-4 1-2-4-4 1-1-2-4 1-2-4-5 2-4-4-5 4-4-5-6 3-4-5-6 3-4-4-6 3-3-4-4 1-3-4-4 1-2-3-4 1-2-3-5 2-6-6-6 2-5-6-6 2-5-5-6 2-5-5-5 1-5-5-5 4-5-5-5 4-4-5-5 4-4-4-5 4-4-4-4 2-4-4-4 2-2-4-4 1-2-2-4 2-2-4-5 2-4-5-5 4-5-5-6 1-4-5-6 1-3-4-6 1-3-3-4 1-1-3-4 1-3-4-5 1-3-3-5 2-2-6-6 2-2-5-6 2-2-5-5 1-2-5-5 1-1-5-5 1-4-5-5 1-4-4-5 1-4-4-4 4-4-4-6 2-4-4-6 2-2-4-6 2-2-3-4 2-3-4-5 2-3-5-5 3-5-5-6 1-3-5-6 1-3-3-6 1-2-3-3 1-1-3-3 1-1-3-5 1-3-5-5 2-2-2-6 2-2-2-5 1-2-2-5 1-1-2-5 1-1-1-5 1-1-4-5 1-1-4-4 1-4-4-6 4-4-6-6 2-4-6-6 2-3-4-6 2-3-3-4 3-3-4-5 3-3-5-5 3-3-5-6 3-5-6-6 1-3-6-6 1-2-3-6 1-1-3-6 1-1-5-6 1-5-5-6 2-2-2-4 2-2-2-3 1-2-2-3 1-1-2-3 1-1-1-3 1-1-1-4 1-1-4-6 1-4-6-6 4-6-6-6 3-4-6-6 3-3-4-6 3-3-3-4 3-3-3-5 2-3-3-5 2-3-3-6 2-3-5-6 2-3-6-6 1-2-6-6 1-1-2-6 1-2-5-6 1-5-6-6 2-2-2-2 1-2-2-2 1-1-2-2 1-1-1-2 1-1-1-1 1-1-1-6 1-1-6-6 1-6-6-6 3-6-6-6 3-3-6-6 3-3-3-6 3-3-3-3 1-3-3-3 2-3-3-3 2-2-3-3 2-2-3-5 2-2-3-6 1-2-2-6 1-2-4-6 2-4-5-6 4-5-6-6

Rectangle 18x7

With multisets from 1..6
 2-2-2-4 2-2-4-6 2-2-6-6 2-5-6-6 5-5-6-6 1-5-5-6 1-4-5-5 1-2-4-5 1-2-4-6 1-4-6-6 1-6-6-6 6-6-6-6 5-6-6-6 1-5-6-6 1-2-6-6 1-1-6-6 1-1-1-6 1-1-1-4 2-2-2-3 2-2-2-6 2-2-5-6 2-5-5-6 5-5-5-6 4-5-5-6 2-4-5-5 2-2-4-5 2-4-5-6 4-5-6-6 4-6-6-6 2-6-6-6 3-6-6-6 3-5-6-6 1-3-6-6 1-1-3-6 1-1-5-6 1-1-4-6 2-2-2-2 2-2-2-5 2-2-5-5 2-5-5-5 5-5-5-5 4-5-5-5 4-4-5-5 2-4-4-5 2-4-4-6 4-4-5-6 4-4-6-6 2-4-6-6 3-4-6-6 3-3-6-6 2-3-6-6 1-2-3-6 1-2-5-6 1-1-2-6 1-2-2-2 1-2-2-5 1-2-5-5 1-5-5-5 3-5-5-5 3-4-5-5 3-4-4-5 4-4-4-5 4-4-4-6 1-4-4-6 3-4-4-6 2-3-4-6 3-3-4-6 3-3-3-6 2-3-3-6 1-2-3-3 1-2-3-5 1-1-2-3 1-1-2-2 1-1-2-5 1-1-5-5 1-3-5-5 3-3-5-5 3-3-4-5 3-3-4-4 3-4-4-4 4-4-4-4 1-4-4-4 1-3-4-4 1-3-4-6 1-3-3-4 1-3-3-6 3-3-5-6 2-3-3-5 2-3-4-5 1-2-3-4 1-1-1-2 1-1-1-5 1-1-3-5 1-3-3-5 3-3-3-5 3-3-3-4 2-3-3-4 2-3-4-4 2-4-4-4 1-2-4-4 1-1-4-4 1-1-3-4 1-3-4-5 1-3-5-6 3-5-5-6 2-3-5-5 2-2-3-5 1-2-2-3 1-1-1-1 1-1-1-3 1-1-3-3 1-3-3-3 3-3-3-3 2-3-3-3 2-2-3-3 2-2-3-4 2-2-4-4 1-2-2-4 1-1-2-4 1-1-4-5 1-4-4-5 1-4-5-6 3-4-5-6 2-3-5-6 2-2-3-6 1-2-2-6

The rectangle 14x9 has the shortest perimeter and the highest number of touching sides.

The spiral has the lowest number of touching sides among all shown figures with these multisets.

## n=7, k=4, 210 multisets

The pieces are made from foam rubber sticked on white squares. In the upper part there are seven columns with all pieces with three or two same colored elements of one color. In the lower section we have 7C2=21 pieces with two pairs of same colored elements, seven pieces with all elements same colored and 7C4=35 pieces with all elements different.

The 15x14 rectangle was constructed using the 10x7 rectangle made of multisets from five colors as shown above. It was rather hard to get the solution because this rectangle is an almost square with a maximum of touching sides.

Rectangle 70x3
 2-3-3-3 3-3-3-5 3-3-4-5 3-4-4-5 4-4-4-5 4-4-5-6 4-4-6-6 2-4-6-6 2-2-6-6 1-2-2-6 1-1-2-2 1-2-2-4 2-2-4-5 2-4-5-6 4-5-6-6 4-6-6-6 3-4-6-6 3-3-6-6 2-3-6-6 1-2-3-6 1-1-2-3 1-1-2-4 1-1-4-4 1-1-4-6 1-4-6-6 1-2-4-6 1-2-3-4 1-2-4-5 1-1-4-5 1-1-5-5 1-5-5-6 1-2-5-5 2-4-5-5 4-5-5-6 3-4-5-6 2-3-4-6 2-2-3-4 2-2-3-6 2-3-5-6 3-5-6-6 1-5-6-6 1-4-5-6 1-4-6-7 1-6-7-7 1-5-7-7 1-3-7-7 1-4-7-7 4-4-7-7 2-4-4-7 2-4-7-7 2-7-7-7 1-2-7-7 2-3-7-7 3-6-7-7 3-3-6-7 3-5-6-7 5-5-6-7 2-5-6-7 2-5-7-7 2-2-7-7 2-2-2-7 2-2-6-7 2-6-7-7 2-6-6-7 6-6-7-7 5-6-7-7 1-5-6-7 1-3-5-7 1-3-3-7 3-3-3-7 3-3-3-6 1-3-3-3 1-3-3-4 1-3-4-4 1-4-4-4 4-4-4-6 2-4-4-6 2-2-4-6 2-2-2-6 1-2-2-2 1-2-2-3 1-2-2-5 2-2-2-5 2-2-5-6 2-5-6-6 2-6-6-6 3-6-6-6 1-3-6-6 1-2-6-6 1-1-2-6 1-1-1-2 1-1-1-4 1-1-3-4 1-1-3-6 1-3-4-6 1-4-4-6 1-2-4-4 1-4-4-5 1-4-5-5 1-5-5-5 5-5-5-6 2-5-5-5 2-3-5-5 3-5-5-6 3-4-5-5 2-3-4-5 2-3-3-4 2-3-3-6 3-3-5-6 1-3-5-6 1-1-5-6 1-2-5-6 1-2-6-7 1-1-6-7 1-1-5-7 1-1-3-7 1-3-4-7 3-4-4-7 4-4-5-7 4-5-7-7 5-7-7-7 1-7-7-7 3-7-7-7 3-3-7-7 3-3-5-7 3-5-5-7 1-5-5-7 2-5-5-7 1-2-5-7 2-2-5-7 2-2-4-7 2-2-3-7 2-3-6-7 3-6-6-7 6-6-6-7 5-6-6-7 4-5-6-7 3-4-5-7 3-3-4-7 2-3-3-7 3-3-3-3 3-3-3-4 3-3-4-4 3-4-4-4 4-4-4-4 2-4-4-4 2-2-4-4 2-2-2-4 2-2-2-2 2-2-2-3 2-2-3-3 2-2-3-5 2-2-5-5 2-5-5-6 5-5-6-6 5-6-6-6 6-6-6-6 1-6-6-6 1-1-6-6 1-1-1-6 1-1-1-1 1-1-1-3 1-1-3-3 1-3-3-6 3-3-4-6 3-4-4-6 2-3-4-4 2-4-4-5 4-4-5-5 4-5-5-5 5-5-5-5 3-5-5-5 3-3-5-5 1-3-5-5 1-3-4-5 1-2-3-5 2-3-3-5 1-2-3-3 1-3-3-5 1-1-3-5 1-1-1-5 1-1-2-5 1-1-2-7 1-1-7-7 1-1-1-7 1-1-4-7 1-4-4-7 4-4-4-7 4-4-6-7 4-6-7-7 6-7-7-7 7-7-7-7 4-7-7-7 3-4-7-7 3-5-7-7 5-5-7-7 5-5-5-7 4-5-5-7 1-4-5-7 2-4-5-7 1-2-4-7 1-2-2-7 1-2-3-7 1-3-6-7 1-6-6-7 4-6-6-7 2-4-6-7 3-4-6-7 2-3-4-7 2-3-5-7

Rectangle 42x5
 3-5-5-5 3-4-5-5 1-4-5-5 1-2-4-5 1-4-4-5 1-4-4-4 1-2-4-4 1-2-2-4 2-2-2-4 2-2-2-2 2-2-2-3 2-2-3-3 2-3-3-4 3-3-4-5 3-3-5-6 3-3-6-6 3-6-6-6 6-6-6-6 5-6-6-6 4-5-6-6 4-5-5-6 5-5-5-6 2-5-5-6 2-2-5-6 2-2-2-6 2-2-2-7 2-2-6-7 2-6-6-7 6-6-6-7 4-6-6-7 4-4-6-7 4-4-4-7 1-4-4-7 3-4-4-7 3-4-6-7 1-3-6-7 3-6-7-7 2-3-7-7 2-2-7-7 2-2-5-7 2-2-3-7 2-2-4-7 3-3-5-5 2-3-5-5 1-3-5-5 1-2-3-5 1-3-4-5 1-3-4-4 1-2-3-4 1-2-2-3 1-2-2-2 2-2-2-5 2-2-3-5 2-2-3-4 2-3-4-5 3-4-4-5 3-4-5-6 3-4-6-6 4-6-6-6 1-6-6-6 2-6-6-6 2-5-6-6 5-5-6-6 3-5-5-6 1-5-5-6 1-2-5-6 1-2-2-6 1-2-2-7 1-2-6-7 1-6-6-7 6-6-7-7 4-6-7-7 4-4-7-7 2-4-4-7 4-4-5-7 3-4-5-7 3-5-6-7 3-6-6-7 2-3-6-7 2-6-7-7 1-2-7-7 1-2-5-7 2-3-5-7 2-3-4-7 3-3-3-5 2-3-3-5 1-3-3-5 1-1-3-5 1-1-4-5 1-1-4-4 1-1-2-4 1-1-2-2 1-2-2-5 2-2-5-5 2-2-4-5 2-2-4-4 2-3-4-4 3-3-4-4 3-3-4-6 1-3-4-6 1-4-6-6 1-2-6-6 2-2-6-6 2-3-6-6 3-5-6-6 1-3-5-6 1-5-6-6 1-1-5-6 1-1-2-6 1-1-2-7 1-1-6-7 1-6-7-7 6-7-7-7 4-7-7-7 2-4-7-7 2-4-5-7 4-5-5-7 1-4-5-7 1-5-6-7 5-6-6-7 2-5-6-7 2-4-6-7 1-2-4-7 1-2-3-7 2-3-3-7 3-3-4-7 3-3-3-4 2-3-3-3 1-2-3-3 1-1-2-3 1-1-3-4 1-1-1-4 1-1-1-2 1-1-2-5 1-2-5-5 2-5-5-5 2-4-5-5 2-4-4-5 2-4-4-4 3-4-4-4 3-4-4-6 1-4-4-6 1-4-5-6 1-2-4-6 2-4-6-6 2-3-4-6 2-3-5-6 1-2-3-6 1-3-6-6 1-1-6-6 1-1-1-6 1-1-1-7 1-1-3-7 1-3-7-7 3-7-7-7 2-7-7-7 2-5-7-7 2-5-5-7 5-5-6-7 1-5-5-7 1-5-7-7 5-6-7-7 4-5-6-7 1-4-6-7 1-3-4-7 1-3-3-7 3-3-5-7 3-3-6-7 3-3-3-3 1-3-3-3 1-3-3-4 1-1-3-3 1-1-1-3 1-1-1-1 1-1-1-5 1-1-5-5 1-5-5-5 5-5-5-5 4-5-5-5 4-4-5-5 4-4-4-5 4-4-4-4 4-4-4-6 4-4-6-6 4-4-5-6 2-4-4-6 2-4-5-6 2-2-4-6 2-2-3-6 2-3-3-6 1-3-3-6 1-1-3-6 1-1-4-6 1-1-4-7 1-1-5-7 1-1-7-7 1-7-7-7 7-7-7-7 5-7-7-7 5-5-7-7 5-5-5-7 3-5-5-7 1-3-5-7 3-5-7-7 4-5-7-7 1-4-7-7 3-4-7-7 3-3-7-7 3-3-3-7 3-3-3-6

Rectangle 33x6
 6-6-6-6 5-6-6-6 5-5-6-6 5-5-5-6 5-5-5-5 3-5-5-5 3-4-5-5 3-4-4-5 3-4-4-4 2-3-4-4 1-2-4-4 1-1-2-4 1-2-4-5 2-4-4-5 4-4-5-6 3-4-5-6 3-4-4-6 3-3-4-4 1-3-4-4 1-2-3-4 1-2-3-5 2-3-5-7 2-5-5-7 5-5-5-7 4-5-5-7 4-4-5-7 4-4-4-7 2-4-4-7 2-2-4-7 2-2-2-7 2-2-5-7 2-2-6-7 1-2-6-7 1-4-6-7 3-4-6-7 2-6-6-6 2-5-6-6 2-5-5-6 2-5-5-5 1-5-5-5 4-5-5-5 4-4-5-5 4-4-4-5 4-4-4-4 2-4-4-4 2-2-4-4 1-2-2-4 2-2-4-5 2-4-5-5 4-5-5-6 1-4-5-6 1-3-4-6 1-3-3-4 1-1-3-4 1-3-4-5 1-3-3-5 1-3-5-7 3-5-5-7 5-5-7-7 4-5-7-7 4-4-7-7 3-4-4-7 1-4-4-7 1-2-4-7 1-2-2-7 2-2-7-7 2-2-3-7 2-3-6-7 2-4-6-7 4-4-6-7 2-2-6-6 2-2-5-6 2-2-5-5 1-2-5-5 1-1-5-5 1-4-5-5 1-4-4-5 1-4-4-4 4-4-4-6 2-4-4-6 2-2-4-6 2-2-3-4 2-3-4-5 2-3-5-5 3-5-5-6 1-3-5-6 1-3-3-6 1-2-3-3 1-1-3-3 1-1-3-5 1-3-5-5 1-5-5-7 5-5-6-7 5-6-7-7 5-7-7-7 4-7-7-7 3-4-7-7 1-3-4-7 1-1-4-7 1-1-2-7 1-2-7-7 2-3-7-7 2-3-4-7 2-4-5-7 4-5-6-7 2-2-2-6 2-2-2-5 1-2-2-5 1-1-2-5 1-1-1-5 1-1-4-5 1-1-4-4 1-4-4-6 4-4-6-6 2-4-6-6 2-3-4-6 2-3-3-4 3-3-4-5 3-3-5-5 3-3-5-6 3-5-6-6 1-3-6-6 1-2-3-6 1-1-3-6 1-1-5-6 1-5-5-6 1-5-6-7 5-6-6-7 2-5-6-7 2-5-7-7 2-4-7-7 4-6-7-7 1-4-7-7 1-4-5-7 1-2-5-7 1-2-3-7 2-3-3-7 3-3-4-7 3-4-5-7 3-5-6-7 2-2-2-4 2-2-2-3 1-2-2-3 1-1-2-3 1-1-1-3 1-1-1-4 1-1-4-6 1-4-6-6 4-6-6-6 3-4-6-6 3-3-4-6 3-3-3-4 3-3-3-5 2-3-3-5 2-3-3-6 2-3-5-6 2-3-6-6 1-2-6-6 1-1-2-6 1-2-5-6 1-5-6-6 1-6-6-7 6-6-7-7 2-6-6-7 2-6-7-7 2-7-7-7 6-7-7-7 1-6-7-7 1-5-7-7 1-1-5-7 1-1-3-7 1-3-3-7 3-3-3-7 3-3-5-7 3-5-7-7 2-2-2-2 1-2-2-2 1-1-2-2 1-1-1-2 1-1-1-1 1-1-1-6 1-1-6-6 1-6-6-6 3-6-6-6 3-3-6-6 3-3-3-6 3-3-3-3 1-3-3-3 2-3-3-3 2-2-3-3 2-2-3-5 2-2-3-6 1-2-2-6 1-2-4-6 2-4-5-6 4-5-6-6 4-6-6-7 6-6-6-7 3-6-6-7 3-6-7-7 3-7-7-7 7-7-7-7 1-7-7-7 1-1-7-7 1-1-1-7 1-1-6-7 1-3-6-7 3-3-6-7 3-3-7-7 1-3-7-7

Rectangle 30x7
 1-1-1-1 1-1-1-3 1-1-3-3 1-3-3-3 3-3-3-3 2-3-3-3 2-2-3-3 2-2-3-4 2-2-4-4 1-2-2-4 1-1-2-4 1-1-4-5 1-4-4-5 1-4-5-6 3-4-5-6 2-3-5-6 2-2-3-6 1-2-2-6 2-2-6-7 2-3-6-7 3-3-6-7 3-3-5-7 2-3-5-7 3-5-6-7 1-3-6-7 1-6-6-7 1-4-6-7 4-6-7-7 1-4-7-7 1-3-4-7 1-1-1-2 1-1-1-5 1-1-3-5 1-3-3-5 3-3-3-5 3-3-3-4 2-3-3-4 2-3-4-4 2-4-4-4 1-2-4-4 1-1-4-4 1-1-3-4 1-3-4-5 1-3-5-6 3-5-5-6 2-3-5-5 2-2-3-5 1-2-2-3 2-2-3-7 2-3-3-7 3-3-3-7 3-3-4-7 2-3-4-7 3-4-6-7 3-6-6-7 6-6-6-7 4-6-6-7 4-4-6-7 4-4-7-7 1-4-4-7 1-1-2-2 1-1-2-5 1-1-5-5 1-3-5-5 3-3-5-5 3-3-4-5 3-3-4-4 3-4-4-4 4-4-4-4 1-4-4-4 1-3-4-4 1-3-4-6 1-3-3-4 1-3-3-6 3-3-5-6 2-3-3-5 2-3-4-5 1-2-3-4 1-2-3-7 1-3-3-7 3-3-7-7 3-4-7-7 2-3-7-7 3-6-7-7 6-6-7-7 5-6-6-7 4-5-6-7 2-4-6-7 2-4-4-7 4-4-4-7 1-2-2-2 1-2-2-5 1-2-5-5 1-5-5-5 3-5-5-5 3-4-5-5 3-4-4-5 4-4-4-5 4-4-4-6 1-4-4-6 3-4-4-6 2-3-4-6 3-3-4-6 3-3-3-6 2-3-3-6 1-2-3-3 1-2-3-5 1-1-2-3 1-1-3-7 1-3-5-7 1-3-7-7 3-7-7-7 3-5-7-7 5-6-7-7 2-6-7-7 2-6-6-7 2-5-6-7 2-4-5-7 4-4-5-7 3-4-4-7 2-2-2-2 2-2-2-5 2-2-5-5 2-5-5-5 5-5-5-5 4-5-5-5 4-4-5-5 2-4-4-5 2-4-4-6 4-4-5-6 4-4-6-6 2-4-6-6 3-4-6-6 3-3-6-6 2-3-6-6 1-2-3-6 1-2-5-6 1-1-2-6 1-1-2-7 1-1-5-7 1-5-7-7 5-7-7-7 4-5-7-7 2-5-7-7 1-2-7-7 1-2-6-7 1-5-6-7 1-4-5-7 4-5-5-7 3-4-5-7 2-2-2-3 2-2-2-6 2-2-5-6 2-5-5-6 5-5-5-6 4-5-5-6 2-4-5-5 2-2-4-5 2-4-5-6 4-5-6-6 4-6-6-6 2-6-6-6 3-6-6-6 3-5-6-6 1-3-6-6 1-1-3-6 1-1-5-6 1-1-4-6 1-1-4-7 1-1-6-7 1-6-7-7 6-7-7-7 4-7-7-7 2-4-7-7 1-2-4-7 1-2-2-7 1-2-5-7 1-5-5-7 5-5-5-7 3-5-5-7 2-2-2-4 2-2-4-6 2-2-6-6 2-5-6-6 5-5-6-6 1-5-5-6 1-4-5-5 1-2-4-5 1-2-4-6 1-4-6-6 1-6-6-6 6-6-6-6 5-6-6-6 1-5-6-6 1-2-6-6 1-1-6-6 1-1-1-6 1-1-1-4 1-1-1-7 1-1-7-7 1-7-7-7 7-7-7-7 2-7-7-7 2-2-7-7 2-2-4-7 2-2-2-7 2-2-5-7 2-5-5-7 5-5-7-7 5-5-6-7

Rectangle 21x10

With multisets from 1..7
 5-7-7-7 7-7-7-7 2-7-7-7 2-3-7-7 3-4-7-7 3-3-4-7 2-3-3-7 2-3-5-7 3-3-5-7 2-2-6-7 2-2-2-7 2-2-3-7 2-3-4-7 1-3-4-7 1-1-3-4 1-1-1-4 1-1-1-5 1-1-5-5 1-4-5-5 4-5-5-5 5-5-5-5 6-7-7-7 1-7-7-7 4-7-7-7 3-7-7-7 3-3-7-7 3-3-3-7 3-3-6-7 2-3-6-7 1-2-6-7 1-2-2-7 2-2-7-7 2-2-5-7 2-2-4-7 1-2-4-7 1-2-3-4 1-1-2-4 1-1-2-5 1-2-5-5 1-5-5-5 2-5-5-5 3-5-5-5 5-6-7-7 1-6-7-7 4-6-7-7 3-6-7-7 3-5-7-7 3-3-5-7 1-3-3-7 1-2-3-7 1-1-2-7 1-2-7-7 2-5-7-7 2-4-5-7 2-4-7-7 2-4-4-7 2-3-4-4 1-2-4-4 1-2-4-5 1-2-3-5 1-3-5-5 2-3-5-5 3-4-5-5 6-6-7-7 2-6-7-7 2-4-6-7 3-4-6-7 3-4-5-7 3-5-5-7 1-3-5-7 1-3-6-7 1-1-3-7 1-3-7-7 1-5-7-7 4-5-7-7 4-4-7-7 1-4-4-7 1-3-4-4 1-1-4-4 1-1-4-5 1-1-3-5 1-3-3-5 2-3-3-5 3-3-5-5 6-6-6-7 2-6-6-7 4-6-6-7 4-5-6-7 4-5-5-7 5-5-7-7 1-5-5-7 1-5-6-7 1-1-6-7 1-1-7-7 1-4-7-7 1-4-5-7 4-4-5-7 3-4-4-7 3-4-4-4 1-4-4-4 1-4-4-5 1-3-4-5 1-3-3-4 3-3-4-5 3-3-3-5 1-6-6-7 5-6-6-7 3-6-6-7 3-5-6-7 5-5-6-7 5-5-5-7 2-5-5-7 1-2-5-7 1-1-5-7 1-1-1-7 1-1-4-7 1-4-6-7 4-4-6-7 4-4-4-7 4-4-4-4 4-4-4-5 4-4-5-5 3-4-4-5 3-3-4-4 3-3-3-4 3-3-3-3 1-5-6-6 5-5-6-6 3-5-6-6 1-3-5-6 1-5-5-6 5-5-5-6 2-5-5-6 1-2-5-6 1-1-5-6 1-1-1-6 1-1-4-6 1-4-4-6 4-4-5-6 4-4-4-6 2-4-4-4 2-4-4-5 2-4-5-5 2-3-4-5 2-3-3-4 2-3-3-3 1-3-3-3 2-5-6-6 5-6-6-6 4-5-6-6 1-4-5-6 4-5-5-6 3-5-5-6 2-3-5-6 1-2-3-6 1-1-3-6 1-1-6-6 1-1-2-6 1-2-4-6 2-4-5-6 2-4-4-6 2-2-4-4 2-2-4-5 2-2-5-5 2-2-3-5 2-2-3-3 1-2-3-3 1-1-3-3 2-4-6-6 4-6-6-6 1-4-6-6 1-3-4-6 3-4-5-6 3-3-5-6 2-3-3-6 2-3-6-6 1-3-6-6 1-6-6-6 1-2-6-6 1-2-2-6 2-2-5-6 2-2-4-6 1-2-2-4 2-2-2-4 2-2-2-5 1-2-2-5 1-2-2-3 1-1-2-3 1-1-1-3 2-3-4-6 3-4-6-6 4-4-6-6 3-4-4-6 3-3-4-6 1-3-3-6 3-3-3-6 3-3-6-6 3-6-6-6 6-6-6-6 2-6-6-6 2-2-6-6 2-2-2-6 2-2-3-6 2-2-3-4 2-2-2-3 2-2-2-2 1-2-2-2 1-1-2-2 1-1-1-2 1-1-1-1

## n=8, k=4, 330 multisets

Rectangle 110x3. It's an extension of the 70x3 rectangle with multisets of 7 items.

 2-3-3-3 3-3-3-5 3-3-4-5 3-4-4-5 4-4-4-5 4-4-5-6 4-4-6-6 2-4-6-6 2-2-6-6 1-2-2-6 1-1-2-2 1-2-2-4 2-2-4-5 2-4-5-6 4-5-6-6 4-6-6-6 3-4-6-6 3-3-6-6 2-3-6-6 1-2-3-6 1-1-2-3 1-1-2-4 1-1-4-4 1-1-4-6 1-4-6-6 1-2-4-6 1-2-3-4 1-2-4-5 1-1-4-5 1-1-5-5 1-5-5-6 1-2-5-5 2-4-5-5 4-5-5-6 3-4-5-6 2-3-4-6 2-2-3-4 2-2-3-6 2-3-5-6 3-5-6-6 1-5-6-6 1-4-5-6 1-4-6-7 1-6-7-7 1-5-7-7 1-3-7-7 1-4-7-7 4-4-7-7 2-4-4-7 2-4-7-7 2-7-7-7 1-2-7-7 2-3-7-7 3-6-7-7 3-3-6-7 3-5-6-7 5-5-6-7 2-5-6-7 2-5-7-7 2-2-7-7 2-2-2-7 2-2-6-7 2-6-7-7 2-6-6-7 6-6-7-7 5-6-7-7 1-5-6-7 1-3-5-7 1-3-3-7 3-3-3-7 3-3-3-8 3-3-8-8 3-8-8-8 8-8-8-8 2-8-8-8 5-8-8-8 5-5-8-8 5-5-5-8 4-5-5-8 5-5-6-8 5-6-6-8 6-6-8-8 6-6-6-8 4-6-6-8 6-6-7-8 6-7-8-8 7-7-8-8 7-7-7-8 2-7-7-8 5-7-7-8 3-5-7-8 3-4-7-8 3-4-4-8 4-4-8-8 2-4-4-8 2-2-4-8 2-2-8-8 2-2-2-8 2-2-3-8 1-2-3-8 2-3-4-8 2-4-6-8 4-6-8-8 5-6-8-8 4-5-8-8 1-4-5-8 4-5-6-8 1-5-6-8 1-1-5-8 1-1-1-8 3-3-3-6 1-3-3-3 1-3-3-4 1-3-4-4 1-4-4-4 4-4-4-6 2-4-4-6 2-2-4-6 2-2-2-6 1-2-2-2 1-2-2-3 1-2-2-5 2-2-2-5 2-2-5-6 2-5-6-6 2-6-6-6 3-6-6-6 1-3-6-6 1-2-6-6 1-1-2-6 1-1-1-2 1-1-1-4 1-1-3-4 1-1-3-6 1-3-4-6 1-4-4-6 1-2-4-4 1-4-4-5 1-4-5-5 1-5-5-5 5-5-5-6 2-5-5-5 2-3-5-5 3-5-5-6 3-4-5-5 2-3-4-5 2-3-3-4 2-3-3-6 3-3-5-6 1-3-5-6 1-1-5-6 1-2-5-6 1-2-6-7 1-1-6-7 1-1-5-7 1-1-3-7 1-3-4-7 3-4-4-7 4-4-5-7 4-5-7-7 5-7-7-7 1-7-7-7 3-7-7-7 3-3-7-7 3-3-5-7 3-5-5-7 1-5-5-7 2-5-5-7 1-2-5-7 2-2-5-7 2-2-4-7 2-2-3-7 2-3-6-7 3-6-6-7 6-6-6-7 5-6-6-7 4-5-6-7 3-4-5-7 3-3-4-7 2-3-3-7 2-3-3-8 3-3-4-8 3-4-8-8 4-8-8-8 1-8-8-8 1-5-8-8 5-7-8-8 5-5-7-8 2-5-5-8 3-5-5-8 3-5-6-8 3-6-8-8 3-6-6-8 2-6-6-8 1-6-6-8 1-6-7-8 1-7-7-8 4-7-7-8 3-7-7-8 6-7-7-8 5-6-7-8 4-5-7-8 4-4-5-8 4-4-4-8 1-4-4-8 1-2-4-8 1-2-2-8 2-2-5-8 2-2-7-8 1-2-7-8 2-4-7-8 2-4-8-8 2-6-8-8 2-5-6-8 2-4-5-8 3-4-5-8 3-4-6-8 1-3-6-8 1-1-3-8 1-1-8-8 3-3-3-3 3-3-3-4 3-3-4-4 3-4-4-4 4-4-4-4 2-4-4-4 2-2-4-4 2-2-2-4 2-2-2-2 2-2-2-3 2-2-3-3 2-2-3-5 2-2-5-5 2-5-5-6 5-5-6-6 5-6-6-6 6-6-6-6 1-6-6-6 1-1-6-6 1-1-1-6 1-1-1-1 1-1-1-3 1-1-3-3 1-3-3-6 3-3-4-6 3-4-4-6 2-3-4-4 2-4-4-5 4-4-5-5 4-5-5-5 5-5-5-5 3-5-5-5 3-3-5-5 1-3-5-5 1-3-4-5 1-2-3-5 2-3-3-5 1-2-3-3 1-3-3-5 1-1-3-5 1-1-1-5 1-1-2-5 1-1-2-7 1-1-7-7 1-1-1-7 1-1-4-7 1-4-4-7 4-4-4-7 4-4-6-7 4-6-7-7 6-7-7-7 7-7-7-7 4-7-7-7 3-4-7-7 3-5-7-7 5-5-7-7 5-5-5-7 4-5-5-7 1-4-5-7 2-4-5-7 1-2-4-7 1-2-2-7 1-2-3-7 1-3-6-7 1-6-6-7 4-6-6-7 2-4-6-7 3-4-6-7 2-3-4-7 2-3-5-7 2-3-7-8 3-3-7-8 3-7-8-8 7-8-8-8 6-8-8-8 1-6-8-8 1-7-8-8 1-5-7-8 1-5-5-8 1-3-5-8 3-5-8-8 2-3-8-8 2-3-6-8 2-2-6-8 1-2-6-8 1-1-6-8 1-1-7-8 1-4-7-8 1-3-7-8 3-6-7-8 2-6-7-8 4-6-7-8 4-4-7-8 4-4-6-8 1-4-6-8 1-1-4-8 1-1-2-8 1-2-5-8 2-5-7-8 2-7-8-8 4-7-8-8 1-4-8-8 1-2-8-8 2-5-8-8 2-3-5-8 3-3-5-8 3-3-6-8 1-3-3-8 1-3-4-8 1-3-8-8

Rectangle 66x5
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Rectangle 55x6
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Rectangle 33x10

With multisets from 1..8
 1-1-1-1 1-1-1-2 1-1-2-2 1-2-2-2 2-2-2-2 2-2-2-3 2-2-3-4 2-2-3-6 2-2-2-6 2-2-6-6 2-6-6-6 6-6-6-6 3-6-6-6 3-3-6-6 3-3-3-6 1-3-3-6 3-3-4-6 3-4-4-6 4-4-6-6 3-4-6-6 2-3-4-6 3-4-6-8 4-4-6-8 2-4-4-8 4-4-4-8 4-4-8-8 4-4-5-8 4-5-7-8 4-7-8-8 2-4-8-8 2-6-8-8 1-2-6-8 1-2-4-8 1-1-1-3 1-1-2-3 1-2-2-3 1-2-2-5 2-2-2-5 2-2-2-4 1-2-2-4 2-2-4-6 2-2-5-6 1-2-2-6 1-2-6-6 1-6-6-6 1-3-6-6 2-3-6-6 2-3-3-6 3-3-5-6 3-4-5-6 1-3-4-6 1-4-6-6 4-6-6-6 2-4-6-6 4-6-6-8 2-4-6-8 2-3-4-8 3-4-4-8 1-4-4-8 4-4-7-8 4-7-7-8 2-4-7-8 2-2-4-8 2-2-6-8 2-5-6-8 2-4-5-8 1-1-3-3 1-2-3-3 2-2-3-3 2-2-3-5 2-2-5-5 2-2-4-5 2-2-4-4 2-4-4-6 2-4-5-6 1-2-4-6 1-1-2-6 1-1-6-6 1-1-3-6 1-2-3-6 2-3-5-6 3-5-5-6 4-5-5-6 1-4-5-6 4-5-6-6 5-6-6-6 2-5-6-6 2-6-6-8 2-3-6-8 2-3-3-8 3-3-4-8 1-3-4-8 3-4-7-8 3-7-7-8 2-3-7-8 2-2-3-8 2-2-2-8 2-2-5-8 1-2-5-8 1-3-3-3 2-3-3-3 2-3-3-4 2-3-4-5 2-4-5-5 2-4-4-5 2-4-4-4 4-4-4-6 4-4-5-6 1-4-4-6 1-1-4-6 1-1-1-6 1-1-5-6 1-2-5-6 2-5-5-6 5-5-5-6 1-5-5-6 1-3-5-6 3-5-6-6 5-5-6-6 1-5-6-6 5-6-6-8 3-5-6-8 3-3-5-8 3-3-3-8 1-3-3-8 1-3-7-8 1-7-7-8 2-7-7-8 2-2-7-8 2-2-8-8 1-2-2-8 1-2-3-8 3-3-3-3 3-3-3-4 3-3-4-4 3-4-4-5 4-4-5-5 4-4-4-5 4-4-4-4 4-4-4-7 4-4-6-7 1-4-6-7 1-1-4-7 1-1-1-7 1-1-5-7 1-2-5-7 2-5-5-7 5-5-5-7 5-5-6-7 3-5-6-7 3-6-6-7 5-6-6-7 1-6-6-7 1-6-6-8 1-3-6-8 3-3-6-8 3-3-8-8 3-3-7-8 3-5-7-8 5-7-7-8 2-5-7-8 2-7-8-8 1-2-8-8 1-1-2-8 1-1-3-8 3-3-3-5 3-3-4-5 1-3-3-4 1-3-4-5 1-4-4-5 1-4-4-4 3-4-4-4 3-4-4-7 4-4-5-7 1-4-5-7 1-4-7-7 1-1-7-7 1-1-6-7 1-5-6-7 1-5-5-7 5-5-7-7 4-5-5-7 4-5-6-7 4-6-6-7 2-6-6-7 6-6-6-7 6-6-6-8 3-6-6-8 3-6-8-8 3-4-8-8 3-7-8-8 5-7-8-8 5-5-7-8 1-5-7-8 1-7-8-8 1-1-8-8 1-1-1-8 1-1-6-8 3-3-5-5 2-3-3-5 1-3-3-5 1-1-3-5 1-1-4-5 1-1-4-4 1-3-4-4 1-4-4-7 4-4-7-7 4-5-7-7 1-5-7-7 1-3-7-7 1-1-3-7 1-3-6-7 1-3-5-7 3-5-5-7 3-4-5-7 3-4-6-7 2-4-6-7 2-6-7-7 6-6-7-7 6-6-7-8 6-6-8-8 1-6-8-8 1-4-8-8 1-3-8-8 3-5-8-8 3-5-5-8 1-3-5-8 1-5-8-8 1-1-5-8 1-1-4-8 1-1-7-8 3-4-5-5 2-3-5-5 1-3-5-5 1-2-3-5 1-2-4-5 1-2-4-4 2-3-4-4 2-4-4-7 2-4-7-7 2-4-5-7 2-5-7-7 1-2-7-7 1-1-2-7 1-2-3-7 1-3-3-7 3-3-5-7 3-5-7-7 3-6-7-7 4-6-7-7 1-6-7-7 5-6-7-7 5-6-7-8 5-6-8-8 4-6-8-8 4-8-8-8 3-8-8-8 2-3-8-8 2-3-5-8 3-4-5-8 4-5-8-8 1-4-5-8 1-4-7-8 1-2-7-8 3-5-5-5 2-5-5-5 1-5-5-5 1-2-5-5 1-1-2-5 1-1-2-4 1-2-3-4 1-2-4-7 2-2-4-7 2-2-5-7 2-2-7-7 1-2-2-7 1-2-6-7 2-3-6-7 3-3-6-7 3-3-3-7 3-3-7-7 3-7-7-7 4-7-7-7 1-7-7-7 6-7-7-7 6-7-7-8 6-7-8-8 6-8-8-8 1-8-8-8 2-8-8-8 2-5-8-8 2-5-5-8 4-5-5-8 4-5-6-8 1-4-6-8 4-6-7-8 2-6-7-8 5-5-5-5 4-5-5-5 1-4-5-5 1-1-5-5 1-1-1-5 1-1-1-4 1-1-3-4 1-3-4-7 2-3-4-7 2-2-3-7 2-2-2-7 2-2-6-7 3-3-5-7 2-3-5-7 2-3-3-7 3-3-4-7 3-4-7-7 2-3-7-7 2-7-7-7 7-7-7-7 5-7-7-7 7-7-7-8 7-7-8-8 7-8-8-8 8-8-8-8 5-8-8-8 5-5-8-8 5-5-5-8 1-5-5-8 5-5-6-8 1-5-6-8 2-3-3-8 3-6-7-8

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