MinT - Information on Result #1179124

Information on Result #1179124

Digital (18, 27, 40)-net over F₂, using net defined by OOA based on linear OOA(2²⁷, 40, F₂, 9, 9) (dual of [(40, 9), 333, 10]-NRT-code), using

appending kth column [i] based on linear OOA(2²⁷, 40, F₂, 8, 9) (dual of [(40, 8), 293, 10]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁹, 23, F₂, 8, 4) (dual of [(23, 8), 175, 5]-NRT-code), using
    - appending 4 arbitrary columns [i] based on linear OOA(2⁹, 23, F₂, 4, 4) (dual of [(23, 4), 83, 5]-NRT-code), using
      - appending kth column [i] based on linear OOA(2⁹, 23, F₂, 3, 4) (dual of [(23, 3), 60, 5]-NRT-code), using
        extracting embedded OOA [i] based on digital (5, 9, 23)-net over F₂, using
        linear code embedding found in a computer search [i]
  2. linear OOA(2¹⁸, 20, F₂, 8, 9) (dual of [(20, 8), 142, 10]-NRT-code), using
    - extracting embedded OOA [i] based on digital (9, 18, 20)-net over F₂, using
      - linear code embedding found in a computer search [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	Digital (216, 234, 932107)-net over F₂	[i]		(u,Â u+v)-Construction for Nets
2	Digital (216, 235, 932106)-net over F₂	[i]		(u,Â u+v)-Construction for Nets