MinT - Information on Result #1180424

Information on Result #1180424

Digital (31, 44, 57)-net over F₂, using net defined by OOA based on linear OOA(2⁴⁴, 57, F₂, 18, 13) (dual of [(57, 18), 982, 14]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(2⁴⁴, 58, F₂, 6, 13) (dual of [(58, 6), 304, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹⁵, 36, F₂, 6, 6) (dual of [(36, 6), 201, 7]-NRT-code), using
    - appending kth column [i] based on linear OOA(2¹⁵, 36, F₂, 5, 6) (dual of [(36, 5), 165, 7]-NRT-code), using
      - extracting embedded OOA [i] based on digital (9, 15, 36)-net over F₂, using
        linear code embedding found in a computer search [i]
  2. linear OOA(2²⁹, 29, F₂, 6, 13) (dual of [(29, 6), 145, 14]-NRT-code), using
    - extracting embedded OOA [i] based on digital (16, 29, 29)-net over F₂, using
      - a shift-net [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2⁴⁴, 49, F₂, 3, 13) (dual of [(49, 3), 103, 14]-NRT-code)	[i]		Extracting Embedded OOA
2	Linear OOA(2⁴⁴, 49, F₂, 4, 13) (dual of [(49, 4), 152, 14]-NRT-code)	[i]
3	Linear OOA(2⁴⁴, 49, F₂, 5, 13) (dual of [(49, 5), 201, 14]-NRT-code)	[i]
4	Linear OOA(2⁴⁴, 49, F₂, 6, 13) (dual of [(49, 6), 250, 14]-NRT-code)	[i]