MinT - Information on Result #1180166

Information on Result #1180166

Digital (25, 37, 45)-net over F₂, using net defined by OOA based on linear OOA(2³⁷, 45, F₂, 18, 12) (dual of [(45, 18), 773, 13]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(2³⁷, 46, F₂, 6, 12) (dual of [(46, 6), 239, 13]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹², 21, F₂, 6, 6) (dual of [(21, 6), 114, 7]-NRT-code), using
    - appending kth column [i] based on linear OOA(2¹², 21, F₂, 5, 6) (dual of [(21, 5), 93, 7]-NRT-code), using
      - extracting embedded OOA [i] based on digital (6, 12, 21)-net over F₂, using
        linear code embedding found in a computer search [i]
  2. linear OOA(2²⁵, 25, F₂, 6, 12) (dual of [(25, 6), 125, 13]-NRT-code), using
    - extracting embedded OOA [i] based on digital (13, 25, 25)-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(2³⁷, 41, F₂, 2, 12) (dual of [(41, 2), 45, 13]-NRT-code)	[i]		Extracting Embedded OOA
2	Linear OOA(2³⁷, 41, F₂, 3, 12) (dual of [(41, 3), 86, 13]-NRT-code)	[i]
3	Linear OOA(2³⁷, 41, F₂, 4, 12) (dual of [(41, 4), 127, 13]-NRT-code)	[i]
4	Linear OOA(2³⁷, 41, F₂, 5, 12) (dual of [(41, 5), 168, 13]-NRT-code)	[i]
5	Linear OOA(2³⁷, 41, F₂, 6, 12) (dual of [(41, 6), 209, 13]-NRT-code)	[i]